# OpenLab Assignment 2: Write a question for the first exam

UPDATE 2: LaTeX power users.  Advanced users can check out my additional $\LaTeX$ notes at the bottom of this post.

UPDATE: LaTeX tester.  Want to test out your LaTeX code before you post it in a comment?  There is a LaTeX tester here, where you can type in your formula, hit the button, and see how it looks: http://samples.geekality.net/latex/

NOTE:  When you use the test, do NOT include the dollar signs or the word “latex” — just include the stuff in between.

Assignment (due at midnight on Monday, February 20) .  Create a problem that could appear on the first exam, and post it in a comment as a reply to this assignment.  It should satisfy the following:

1. It can be from anything we have studied so far this semester, from the first day of class up through Section 6.1, Areas Between Curves.
2. It must be a reasonable exam problem — not too easy, not crazy hard (I will be the final judge of what counts as a “reasonable exam problem”). Make sure that you can solve your problem.  For ideas, look at the homework assignments, the review sheet, the group work from class, your notes, and so on (you can use these sources as inspiration, but please don’t copy problems from them directly).  If you wish, you can also ask short-answer, explanatory type questions, like  “Explain in your own words ….” or “Why does …” or “What’s the difference between  xxx and yyy?”.  Bonus points for creative questions!
3. It must contain some kind of mathematical symbols, which must be posted using correct mathematical notation.  How do you do this?  See below.

Extra credit.  Solve one of your classmates’ questions, and post the solution as a reply. Your solution MUST be posted using correct mathematical notation.

What’s the point of this assignment?  Two things:  First, to make you think about what kinds of problems will be on the exam — and creating a problem forces you to consider this from a different perspective (what should be on the exam?) than simply practicing problems.  Second, I want you to start learning how to type mathematics on the OpenLab — how do make integral signs, exponents, square roots, and so on?

Typing math on the OpenLab.  This is not hard — BUT it takes a little getting used to.  Here’s an example. If you type this into a comment:

Here is an integral:  $latex \int x^2 dx$

then (after you post the comment) you should see this:

Here is an integral:  $\int x^2 dx$

Each equation or expression begins with “$latex” and ends with “$”.  The word ‘latex’, which appears after the first dollar sign, does not refer to the rubbery substance used in hospital gloves and sex toys, but rather to the incredibly powerful and awesome math typesetting language $\LaTeX$ created by computer/math god Donald Knuth (and used by basically all math and science professionals in the universe).  In between “$latex” and “$” you type your math — many things you type just as they are, like numbers and variables, but each special math symbol has a special code.  In the example above, we use the code for the integral sign, which is “\int”.  To get the exponent on the $x^2$, use “^” (just like in your graphing calculator).

Here are a few more examples:

 Type this: to get this result: A. $latex \int_0^{\pi} \sin x dx$ $\int_0^{\pi} \sin x dx$ B. $latex \frac{x+1}{x^2 + 5x}$ $\frac{x+1}{x^2 + 5x}$ C. $latex \sqrt{x+1} + \sqrt[5]{x+6}$ $\sqrt{x+1} + \sqrt[5]{x+6}$

Example A (definite integral): Use curly braces “{ }” for grouping things together. On the integral sign, “_” gives a subscript and “^” gives a superscript, which is how we get the 0 and $\pi$ to appear in the correct places. The code for the $\pi$ symbol is “\pi”. For the sine function we use the code “\sin” (which looks nicer than simply typing in the letters “sin”).

Example B (fractions): The code for fractions is “\frac{ }{ }”, with numerator inside the first set of curly braces { } and the denominator in the second set.

Example C (roots and radicals): Square roots and other roots like these $\sqrt{x+1} + \sqrt[5]{x+6}$ are created using the “\sqrt{}” (for square roots) and “\sqrt[n]{ }” (for nth roots)

Hints and suggestions. Don’t start with a complicated formula. Write a comment with a short bit of math in it, and post it to see what it looks like. You can always edit the comment to make changes.

Stuck? Frustrated? Doesn’t look the way you want it to look? Let me know! Send me an email or simply post a question on the OpenLab — let me know what you’ve tried so far, and what you’re trying to accomplish.

For more examples, this link is a pretty good place to start. Want even more symbols? Here you go.

UPDATE: $\LaTeX$ power user section

You guys have been doing a great job typing math into your comments. You can feel free to ignore this, but if you’re interested in a few additional $\LaTeX$ tricks, read on.

1. Making the vertical bar stretch. For the vertical bar, which we use when solving a definite integral (in the step after we take the antiderivative but before we plug in) to keep track of the limits of integration: just use the vertical bar symbol “|” on your keyboard, usually located above the “\” symbol. BUT if you have a fraction or other piece of math that is taller than a single line, the “|” sign looks awfully small by comparison. How do we make it stretch vertically to match the stuff that comes before? We need to indicate to $\LaTeX$ which part of the mathematics we want it to refer to. We do this by enclosing the pertinent parts in the following keywords “\left.” and “\right|” — note that the first, \left., must include the period after it, and the latter, \right|, ends with a |. Here’s an example

$latex \left. \frac{x^2}{2} \right|_0^\pi$

which renders like so:

$\left. \frac{x^2}{2} \right|_0^\pi$

2. That pesky $. If you’re trying to discuss $\LaTeX$ code, instead of actual math, you’ll want to be able to display the stinking dollar sign. BUT the system will automatically compile your code into nice-looking math, making the dollar sign disappear. The solution is to use the HTML code for dollar sign, when you want the dollar sign to appear. The HTML code for$ is &#36; or, said aloud, “ampersand-numbersign-three-six-semicolon”.

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### 244 Responses to OpenLab Assignment 2: Write a question for the first exam

1. Mansoor Baig says:

$\int (5x + 4)^3 dx$

• debitcard says:

u=5x+4
du=5 dx

1/5 $latex\int\(u)^3\du$

The integral of u^3 is u^4/4

1/5 x u^4/4= u^4/20 + C

Substitute u.

1/20 (5x+4)^4 + C

• Jonas Reitz says:

Hi debitcard,
In your response above, you simply need to add a space after the word “latex” — then it will show up correctly. Try editing your comment and see if it works.
-Mr. Reitz

• debitcard says:

Reitz,

I cannot seem to edit my original post.

u=5x+4
du=5 dx

1/5 $\int \(u)^3\du$

The integral of u^3 is u^4/4

1/5 x u^4/4= u^4/20 + C

Substitute u.

1/20 (5x+4)^4 + C

• debitcard, I think you’re looking for this

$u = 5x +4$
$du = 5 dx$
$\frac{1}{5} \int u^3 du \rightarrow \frac{1}{5} \cdot \frac{u^4}{4}$

Substitute u.

$\frac{1}{20} \cdot (5x+4)^4 + C$

• Make sure to put a space between “$latex” and your formulae. Make sure to put the ending “$” directly after your last term– no space in between the two. Take a look at Mr. Reitz’s link to extra symbols and latex structures as well.

• Jonas Reitz says:

mansoorbaig: nice problem, and nice looking notation — thanks for being my first-post-er!

2. lance12 says:

$\int_1^{\4} \{x^3 -5}$

• Jonas Reitz says:

Hi Lance — you’re off to a good start. Two tips — you don’t need the backslash “\” in front of the number 4, or in front of the curly braces {} — get rid of these and I think your formula should display correctly.

• lance12 says:

Professor- I was testing it out. I wasn’t sure how exactly how to delete this post and it just remained there. I’ll make sure to give you a more concrete example. Thank you.

3. $latex\int_a^{\pi}frac\sqrt{2x+1}{x^10+\sqrt18x}dx$

• Jonas Reitz says:

Hi Mirza,
It’s a good start — here’s what to fix:
– insert a space after the word latex
– the keyword “frac” should have a space and a slash in front of it, like this:” \frac”
-Mr. Reitz

• $\int_a^{\pi}\frac\sqrt{2x+1}{x^10+\sqrt{18x}}dx$

• I tried but doesn’t works. I think the problem I wanted to write that’s too complicated. That’s why.

• Jonas Reitz says:

Hi Mirza,

Your problem is fine, and very close to complete. Here’s what your code looked like (for reference):
$latex \int_a^{\pi}\frac\sqrt{2x+1}{x^10+\sqrt{18x}}dx$

I think you are only missing the following — the top of your fraction should be enclosed in curly brackets { }, so the \sqrt{2x+1} should have { } around it. Also, your integral currently goes from “a” to “\pi” — you probably want to replace “a” with a number. Other than that, I think you’re good! Try submitting it again.

Regards,
Mr. Reitz

• $\int_3^{\pi}\frac{\sqrt{2x+1}}{x^10+\sqrt{18x}}dx$

4. Your city is about to be the victim of a flood. In order to prepare for it, you decide to build a dam to stem the flood and then reservoirs to hold the excess water.

To Clarify: There is only one place where the flood can come from– it is one river.

Because you are so awesome, you happen to know that:
Water from the flood will flow inwards at a rate of $-t^2 + 100t$ (or any even function with one absolute maximum and no absolute minimum). t stands for time in minutes; the flow rate is a function of time. Assume that all water flow as a result of this function will count of floodwater and will be carried into a reservoir

How long will the flood last?

$-t^2 +100t = 0 \rightarrow -t^2 = -100t \rightarrow t = 100 , t = 0 \Rightarrow 100$ minutes

Each reservoir can hold $500 ft^3$ of water. How many reservoirs are necessary?

$latex \frac{\int_0^{100} -t^2 +100t}{500 ft^3} • That last part is: $\frac{\int_0^{100} -t^2 +100t}{500 ft^3}$ • Jonas Reitz says: Cool problem! I like the application – creative use of integration. 5. cthoma12 says: $\int \frac{(\ln x)^2}{x}dx$ $u=\ln (x)$ $du= \frac{(1)dx}{x}$ $\int u^2= \frac{1}{3}(u)^3+du$ Just testing it out !! also if you guys want a template to preview your LaTeX use http://wordpress.com/#!/my-blogs/ i’m pretty sure it’s the same platform as open lab so you can hit preview when u try to make a new post 🙂 • Jonas Reitz says: Thanks, Charles — that’s a nice tip (and yes, the OpenLab is based on wordpress so testing it there is a good strategy). If you don’t want to create a new wordpress site just for testing purposes, you can also check out the LaTeX code tester I posted at the top of the assignment (its http://samples.geekality.net/latex/). Your mathematical notation is looking good 🙂 6. $\int_a^{\pi}\frac\sqrt{2x+1}{x^10+\sqrt18x}dx$ 7. shamonie22 says: latex \int_4^{6} \frac{3x^2+\sqrt{x}}{x^2} dx 8. shamonie22 says: $\int_4^{6} \frac{3x^2+\sqrt{x}}{x^2} dx$ • Jonas Reitz says: Nice! • Musaib says: $\int_4^{6}{3} dx+latex \int_4^{6} \frac{1}{x^-3/2} dx$$3x|_4^{6}-2x^-1/2|_4^{6}$3(6-4)-2(6^-1/2-4^-1/2) 6+0.183 6.183 • Musaib says: $\int_4^{6}{3} dx+ \int_4^{6} \frac{1}{x^-3/2} dx$ 3x|_4^{6}-2x^-1/2|_4^{6} 3(6-4)-2(6^-1/2-4^-1/2) 6+0.183 6.183 • Musaib says: $\int_4^{6}{3} dx+ \int_4^{6} \frac{1}{x^-3/2} dx$ 3x|_4^6-2x^-1/2|_4^6 3(6-4)-2(6^-1/2-4^-1/2) 6+0.183 6.183 9. igorekk132 says: \int \frac{x}{\sqrt[5]{x+3}}dx • igorekk132 says: $\int \frac{x}{\sqrt[5]{x+3}}dx$ • igorekk132 says: Answer: $u = x+3 \rightarrow x = u-3$ $du = 1dx$ $\int \frac{u-3}{u^\frac{1}{5}}du$ $\int u^\frac{4}{5}-3u^\frac{-1}{5}du$ $\frac{5}{9}u^\frac{9}{5}-\frac{15}{4}u^\frac{4}{5}$ $\int \frac{5}{9}(x+3)^\frac{9}{5}-\frac{15}{4}(x+3)^\frac{4}{5}+C$ • Jonas Reitz says: Great – but remember, for the extra credit, you have to post an answer to someone else’s problem. • Jonas Reitz says: Tricky one — I like it! 10. $\int_2^{8} \frac{2}{5x^3} dx$ • zbrowne says: \int \frac{2}{5x^3}dx = \frac{2}{5} \int \frac{1}{x^3}dx = – \frac{1}{2x^2} = – \frac{1}{5x^2} \vert_2^{8} \cdots [ (-) \frac{1}{5(8)^2} – (-) \frac{1}{5(2)^2} ] = \frac{3}{64} \equiv 0.046875 • zbrowne says:$latex \int \frac{2}{5x^3}dx =
\frac{2}{5} \int \frac{1}{x^3}dx =
– \frac{1}{2x^2}
= – \frac{1}{5x^2}
\vert_2^{8} \cdots [ (-) \frac{1}{5(8)^2} – (-) \frac{1}{5(2)^2} ]
= \frac{3}{64} \equiv 0.046875$• zbrowne says: $\int \frac{2}{5x^3}dx =$ $\frac{2}{5} \int \frac{1}{x^3}dx =$ $- \frac{1}{2x^2}$ $= - \frac{1}{5x^2}$ $\vert_2^{8} \cdots [ (-) \frac{1}{5(8)^2} - (-)$ $\frac{1}{5(2)^2} ]$ $= \frac{3}{64} \equiv 0.046875$ • Jonas Reitz says: Hi Zekeba — Congrats on working out the LaTeX. You included a lot of it and managed to debug it, nice job! Some minor quibbles with the math but the essence is there, great work. 11. jishan007 says: Jishan Biswas Math 1575 section 6638 $\int x a^x^2 dx$ 12. jishan007 says: Jishan Biswas , mat 1575 sec 6638$latex\int cosx^2 sinx dx$• igorekk132 says: make a space after$latex

• Musaib says:

$\int cosx^2 sinx dx$
Do u mean that?

• Musaib says:

latex \int cos^2x sinx dx
or u mean that?

• jishan007 says:

yes, that’s exactly what it is.
$\int cos^2x sinx dx$.

• Musaib says:

Let u=cos x, then du= -Sin x dx
then $lateu- \int{u^2} du$
$-1/3u^3$
$-1/3cos^3x$

• Musaib says:

Let u=cos x, then du= -Sin x dx
then
$lateu- \int{u^2} du$
-1/3u^3
-1/3cos^3x

• Musaib says:

$u=cos x$
$du=-sin x$
$latex- \int{u^2} du$
$-1/3 u^3$
$-1/3 cos^3 x$

• Musaib says:

$u=cosx$
$du=-sinx$
$latex- \int{u^2} du$
$-1/3 u^3$
$-1/3 cos^3x$

• Jonas Reitz says:

Thanks for the clarification — I was wondering also. Looks good!

• Musaib says:

$\int cos^2x sinx dx$
or This one?

• Musaib says:

u=cosx
du=-sinx
$latex- \int{u^2} du$
-1/3 u^3
-1/3 cos^3x

13. zbrowne says:

Zekeba Browne – MAT 1575 Section 6638 M/W 4:00 pm – 5:40 pm

$\int_1^{2}x^2(x^3+1)^10$

• zbrowne says:

$\int_1^{2}x^2(x^3+1)^10dx$

The last part is to the power of 10 and then dx just to clear any confusion.

• Jonas Reitz says:

I see the dilemma — the “^” doesn’t realize that the 1 and 0 in the number “10” should be grouped together. To force them to both be up in the exponent, enclose them in curly brackets like so: ^{10}.

• $\int _1^{2}x^2(x^3+1)^{10}dx$
Using substitution rule.
u = x^{3} + 1
$\frac{du}{dx}= 3x^2$
du=3x^2 dx
$\frac {1){3} \int _2^{9}u^{10}dx$
$\frac {9^{11}}{33} - \frac {2^{11}}{33}$
950941200.3 – 62.1
950941138.2 (ANS)

• Formula Does not parse
$\frac {1}{3} \int_2^{9}u^{10}dx$

• sorry it should be (du)
$\frac {1}{3} \int_2^{9}u^{10}du$

• zbrowne says:

I see, thanks for the tip Prof. Reitz

14. Musaib says:

$\int_0^{\pi} {x sin{x^2}} dx$

• $\int _{0}^{\pi }\!{{\it xsinx}}^{2}{dx}$
$u = {x}^{2}$
${\frac {{\it du}}{{\it dx}}}=2\,x$
du = 2x dx
$1/2\,\int _{0}^{{\pi }^{2}}\!\sin \left( u \right) {du}$
$-1/2\, \left( \cos \right) \,{\pi }^{2}+1/2\,{\it cos0}$
0.45 + 0.5
0.95 (ANS)

• Jonas Reitz says:

Looks good!

15. $\int_1^{3} \frac{1}{x}{(ln(x))}^2 dx$

• Fengming08 says:

$\ u = lnx$
$\ du = \frac{1}{x} dx$
X=3 u=ln3
X=1 u=ln1
$\int_{ln1}^{ln3} u^2 du$
$\left. \frac{1}{3} u^3 du \right|_{ln1}^{ln3}$
$\frac{1}{3} [(ln3)^3-(ln1)^3]$
0.442(ANS)

• Fengming08 says:

$\ u = lnx$
$\ du = \frac{1}{x} dx$
X=3, u=ln3
X=1, u=ln1
$\int_{ln1}^{ln3} u^2 du$
$\left. \frac{1}{3} u^3 \right|_{ln1}^{ln3}$
$\frac{1}{3} [(ln3)^3-(ln1)^3]$
0.442(ANS)

• Jonas Reitz says:

Great.

16. Fengming08 says:

$\int_0^ \pi cosx^2 sinx dx$

• Fengming08 says:

Fengming Tan
sec#: 6637

• Jonas Reitz says:

Hi Fengming — is it possible you meant $(\cos x)^2 \sin x$? As it stands, I’m not sure I know how to solve it!
Mr. Reitz

• Fengming08 says:

Sorry! The question is:

$\int_0^ \pi cos2x sinx dx$

17. Merino, John says:

$\int_4^{-4} x^3-4 x dx$

18. Joshua Ruiz says:

Joshua Ruiz – Section 6638

$\int_6^{-1} 3x^2 \sec{(x^3+7)} \tan{(x^3+7)} dx$

• Jonas Reitz says:

Hi Joshua — nice integral! BUT there is a problem — the function is not defined on the entire interval from -1 to 6 (or 6 to -1). For example, the secant function is undefined whenever cosine equals 0 (since secant = 1/cosine). To save the problem, either 1) remove the bounds and make it an indefinite integral, or 2) change the bounds to a smaller interval on which both secant and tangent are defined.
Mr. Reitz

• Joshua Ruiz says:

Hmm, I should’ve paid more attention. I couldn’t get a working result testing out the integrals so I’m just going to change the bounds. Thank you for notifying me.
$\int 3x^2 \sec(x^3+7) \tan(x^3+7) dx$

• cthoma12 says:

$latex \int 3x^2 \sec(x^3+1) \tan(x^3+7) dx \\ u=x^3+7 \\ du=3x^2dx \\ now\ you\ must\ resubtitute\\ \int \sec(u) \tan(u) du \\ z=\sec(u) \\ dz= \tan(u) \sec(u) du \\ \int z dz =\sec(u) = \sec(x^3+7)+C$

• cthoma12 says:

$\int 3x^2 \sec(x^3+1) \tan(x^3+7) dx$
$u=x^3+7$
$du=3x^2dx$
$now\ you\ must\ resubtitute$
$\int \sec(u) \tan(u) du$
$z=\sec(u)$
$dz= \tan(u) \sec(u) du$
$\int z dz =\sec(u) = \sec(x^3+7)+C$

19. lance12 says:

$\int_3^{6} \frac{x^4}{x^4 + 7x}$

• Jonas Reitz says:

Hi Lance — this is a nice-looking integral, but I’m not sure how to find the antiderivative (I can’t figure out how to simplify it, and substitution doesn’t seem to work). Am I missing something? Try working it out — if it’s not possible, see if you can make a change of some kind.
Mr. Reitz

20. mmiltz says:

Melissa Miltz, section #6638 (M&W)

$\int\frac{2x^{2}+5\sqrt{x}}{x^{-4}}dx+\int\frac{6x^{2}}{5}dx$

• mmiltz says:

\int\frac{2x^{2}+5\sqrt{x}}{x^{-4}}dx+\int\frac{6x^{2}}{5}dx

21. mmiltz says:

$\int\frac{2x^{2}+5\sqrt{x}}{x^{-4}}dx+\int\frac{6x^{2}}{5}dx$

• Jonas Reitz says:

I like this one — looks nastier than it is, I think!
Mr. Reitz

• mmiltz says:

that’s correct 🙂

22. mendozak says:

$\int_{3}^{9} f{(x)} - g{(x)} dx$

$\int_{9}^{3} f{(x)} - g{(x)} dx$

A. Without any evaluation, explain in your own words which of these problems could yield an area.

B. In your own words, explain the difference between an area and a definite integral.

Khoreece Mendoza
MAT1575 M/W 4PM

• Jonas Reitz says:

Good questions — if you can get these ideas straight, and give a good explanation, you’re well on your way to developing a good intuition for integration.

23. Find the area that is formed by the curve of y = sin x and the x-axis from {0 , π}?

Find the area that is formed by the curve of y = cos x and the x-axis from {-π/2 , π/2} ?

I think these are reasonable problems and believe that if you can solve these, you understand the concepts and i think you’ll be able to do good on the exam?

24. Jonas Reitz says:

Hi Gurpreet — I like these problems a lot! (but I notice you managed to avoid using $\LaTeX$ — post something else or repost with LaTeX for full credit).

Regarding your final question/comment, I’m not sure whether you are referring to a) your two problems above, or b) all the problems appearing in the comments so far. Certainly if you can do all the problems appearing so far, you’ll be well on your way to an A on the exam (but the examples we have are not exhaustive — there will be other things on the exam as well!).

Mr. Reitz

• I read this late but i’ll re-post a new problem. And i was talking about all the comments/questions in the post were useful and you’ll do alright if you can solve them.
Here’s a simple problem.
1) f(x) = \int_0^2 \sqrt{2x + 1} dx

• $f(x) = \int_0^2 \sqrt{2x + 1} dx$

25. bettygeorge says:

bettygeorge MA1575,6638

$latex\int_1^3(1/t^2-1/^4)dt$

26. bettygeorge says:

$\int_1^3(1/t^2-1/t^4)dt$

27. $\int \sqrt{3x^2+7}dx$

• ymerej613 says:

$\int\ \sqrt{5x^2+10} dx$

• ymerej613 says:

sorry i left my question on your post by accident

• Jonas Reitz says:

Same problem as my response to Daniel Edwards — the notation looks good, but I don’t know how to solve it! Try to come up with a solution, and if not see if you can modify the problem to make it work.
Mr. Reitz

• Jonas Reitz says:

The notation looks great — but I’m not sure how to solve it! I could be missing something — do you have a solution? If not, try solving it and think about what you need to add in order to make it work — post an update with the results.
Mr. Reitz

28. vasquez says:

$\int_1^{\2} \sin x dx$

29. vasquez says:

$\int_0^{\pi} \(1+2y)^2 dy$

30. vasquez says:

\int_1^1(1+2y)^2 dy

31. vasquez says:

\int_1^2(1+2y)^2 dy

32. vasquez says:

disregard \int_1^1(1+2y)^2 dy… i made a mistake writting it….

33. endri says:

Endri Domi

$\int_0^2 \sqrt \frac{3}{2x} dx$

34. vasquez says:

$latex\int_1^2(1+2y)^2 dy$

• Jonas Reitz says:

Hi vasquez — good problem! I think you just need to put a space after the work latex, and it should display correctly. Give it a try.
Mr. Reitz

35. ymerej613 says:

Jeremy Li
Mat 1575 6637
$\int\ \sqrt{5x^2+10} dx$

• Jonas Reitz says:

Hi Jeremy — I posted this above but I’ll put it here in case you don’t see it there: The notation looks good, but I don’t know how to solve the problem! Try to come up with a solution, and if not see if you can modify the problem to make it work.
Mr. Reitz

• ymerej613 says:

$\int\ 10 \sqrt{5x^2+10} dx$

36. koshygkoshy says:

Bibin Koshy
Mat 1575 6637
$latex\int_2^{4}\frac{dx}{x^2 + 5x}dx$

37. ashafi says:

$\int x^2 \sqrt{x^3+1} dx$

• Keyla says:

$u=x^3+1$
$du=3x^2dx$
$\frac{du}{3}=x^2dx$

$\frac{1}{3}\int \sqrt{u} du$
$latex\frac{1}{3}\int u^\frac{1}{2} du$

$\frac{1}{3} \cdot \frac{2u^\frac{3}{2}}{3} = \frac{2u^\frac{3}{2}}{9}$

Final Answer: $\frac{2(x^3+1)^\frac{3}{2}}{9}$

• Keyla says:

Keyla Arana, T & Th, 4:05-5:45
Error:
$u=x^3+1$
$du=3x^2dx$
$\frac{du}{3}=x^2dx$

$\frac{1}{3}\int \sqrt{u} du$
$\frac{1}{3}\int u^\frac{1}{2} du$
$\frac{1}{3} \cdot \frac{2u^\frac{3}{2}}{3} = \frac{2u^\frac{3}{2}}{9}$

Final Answer: $\frac{2(x^3+1)^\frac{3}{2}}{9}$

• Keyla says:

• vasquez says:

u= x^3+1
du=3x^2 dx
(1/3)du= x^2 dx

= 1/3 ∫ (u)^1/2 * du
=∫ (1/3) * (2/3) u^3/2 + c
= ∫ 2/9 * ( x^3+1)^3/2 + c

38. koshygkoshy says:

$\int_2^{4}\frac {dx}{x^2 + 5x}$

• Jonas Reitz says:

koshygkoshy — the notation looks fine (if you insert a “dx”), but the integral is hard! I’m not sure how to find the antiderivative — see if you can work it out, and either post a solution or modify the problem. Thanks,
Mr. Reitz

39. bbravo999 says:

Evaluate the indefinite intergal:
$latex\int \frac{cos\sqrt{x}}{\sqrt{x}} dx$

40. bbravo999 says:

$latex\int \frac{cos\sqrt{x}}{\sqrt{x}} dx$

41. bbravo999 says:
42. bbravo999 says:

latex \int \ frac{ cos\ sqrt{x}}{\ sqrt{x}} dx

43. bbravo999 says:

$\int \ frac{ cos\ sqrt{x}}{\ sqrt{x}} dx$

44. bbravo999 says:

$\int \ frac{cos\sqrt{x}}{\sqrt{x}} dx$

45. bbravo999 says:

$\int \frac{cos\sqrt{x}}{\sqrt{x}} dx$

46. bbravo999 says:

Evaluate the indefinite intergal:

$latex\int \frac{cos\sqrt{x}}{\sqrt{x}} dx$

47. bbravo999 says:

Evaluate the indefinite intergal:
$\int \frac{cos\sqrt{x}}{\sqrt{x}} dx$

• Jonas Reitz says:

nice problem, and great debugging work. You did it!
Mr. Reitz

48. takther2009 says:

$latex/int_2^{/3}/frac{dx}{(x-2)}$

• takther2009 says:

What did i do wrong? i cant get the image..
mon/wed 4-540

49. Keyla says:

latex$\int_2^{4x^5}\frac{\sqrt{\sin x+1}}{x^2}dx$

• Keyla says:

Keyla Arana

Why is this always messing up..? Ignore the top one..
$\int_2^{4x^5}\frac{\sqrt{\sin x+1}}{x^2}dx$

• Jonas Reitz says:

Keyla — the notation looks good! But I’m confused by the upper bound of $4x^5$ in the integral. Is it supposed to be there?
Mr. Reitz
(ps. just had a thought — is it a “find the derivative” problem? if so, change each “x” to a “t”, except the $4x^5$)

• Keyla says:

Yes, sorry, i forgot to change the variable, it’s supposed to be t’s.

$\int_2^{4x^5}\frac{\sqrt{\sin t+1}}{t^2}dt$

• Jonas Reitz says:

Great — nice problem! (To clarify, the problem instructions should read “find the derivative”).

50. lance12 says:

$\int_1{^3} \ (x^4+5)^8$

• Jonas Reitz says:

Hi Lance — this is a nice setup, but hard problem! I can’t see how to make substitution work — try it, and modify the question if necessary.
Mr. Reitz

51. tonymei999 says:

Jiarong Mei section 6638

$\e^{x}*sqrt{1+{e^x}} dx$

• tonymei999 says:

$\int e^x * \sqrt{1+e^x} dx$

52. theozeng says:

Theo Zeng section 6638

$\int sec^4 x tan x dx$

• cthoma12 says:

i was told this wasn’t the final asnwer there is more but i’m at a loss

$\int \sec^4(x) \tan(x) dx$
$expand\ since \int \sec^2(x)=\tan^2(x)+1$
$\int (\tan^2(x)+1) (\tan(x)) (\sec^2(x)) dx$
$u=\tan(x)$
$du=\sec^2(x) dx$

$now replace \int u(u^2+1)du= \int (u^3+u)= \int u^3 \int u = \frac{\tan(x)^4}{4} \frac{tan^2(x)}{2}+C$

• cthoma12 says:

actually $\int \sec^2(x)=\tan(x) \\ \sec^2(x)=\tan^2(x)+1$

you cant put a solved integral inside of the unsolved

• Jonas Reitz says:

Great problem but quite tricky, unless you really remember your trig identities!

53. debitcard says:

sub
u= $latex\{e^x+1}$
du= $latex\{e^x dx}$

= $latex\int\sqrt{u}du$

$latex\int\sqrt{u}$ = $latex\frac{2u^3/2}{3}+C$

substitute
$latex\{e^x+1}$
for u

=$latex\frac{2/3(e^x+1)^3/2}/+C$

• debitcard says:

My mistake.. I meant to reply to tonymei999’s post.

I see my work looks perplexed.

54. jishan007 says:

Jishan mat1575, section 6638
$\int_1^4\ln x dx$

• Jonas Reitz says:

Simple looking but deadly! How do we find the antiderivative of ln x? This is worth playing around with, but I would NOT ask it on this exam.
Mr. Reitz

55. stan says:

$\int \sin^4 x dx$

• stan says:

Posted by Stanislav Podolski MAT 1575 – 6638.
Hint: This integral is nor very complicated, but it makes you remember some trigonometry.

• cthoma12 says:

• stan says:

You can start by doing the following:
$\int \(sin^2 x)^2 dx$ =
$\int \frac({1-cos2x}{2})^2$ = …

• stan says:

Formula did not parse(
well basically to start you have to represent sin^4x as (sin^2x)^2.

• Jonas Reitz says:

I agree — definitely a challenge, unless you remember your trig identities!

56. mrcpotter says:

$\int \frac {x^3+1} {x^4+4x} dx$

• Jonas Reitz says:

sweet!

• aman1992 says:

Amanpreet

1/4 $\int \frac 1/u dx$

1/4log (x(x^3+4)) + c

1/4 (log(x^3+4)+log(x))

• aman1992 says:

1/4 $latex \int \frac (1)(u) dx 1/4log (x(x^3+4)) + c 1/4 (log(x^3+4)+log(x)) • aman1992 says: 1/4$latex \int \frac (1/u) dx

1/4log (x(x^3+4)) + c

1/4 (log(x^3+4)+log(x))

57. justinblaize says:

$latex \int lnx+4x^2-2x+4 58. justinblaize says: $\int lnx + 4x^2 - 2x + 4 dx$ • Jonas Reitz says: Look good • justinblaize says: $\int lnx + 4x^2 - 2x +4 dx$ $1/x + 4 * 1/3 x^3 - x^2+ 4x$ $1/x +4/3x^3 -x^2 +4x$ 59. justinblaize says: ^ Find the integral ^ 60. debitcard says: Koonhoi Xie MAT 1575 – 6638. Find the integral between two curves given the function x & x^2 Hint*- Start by finding the point of intersection. Formula is given by$latex\int_a^bf(x)-g(x)dx$• Jonas Reitz says: Koonhoi — looks good! Your formula just needs a space after the word latex. • debitcard says: Thanks, Reitz. Last part is $\int_a^bf(x)-g(x)dx$ 61. kedeshia1111 says: \int\frac{\sin {x}}{1+\sin{x}}dx • Jonas Reitz says: Hi Kedeshia — you just need to put “$latex” at the start and “$” at the end, and your code should display correctly. However, I think your problem is hard — I can’t figure it out! Try it, and see if you can make it work, or make a modification. 62. nazir ahmed math1575-6638 $\int x^3lnx dx$ • Jonas Reitz says: Looks nice, but I can’t figure it out! Am I missing something? Mr. Reitz 63. rupadsingh says: $\int_1^{9}\sqrt\frac{4}{x} dx$ 64. jermin says: $\int \frac{1}{4sinx-3cosx}dx$ • Jonas Reitz says: Cool problem – but I don’t see the solution! Try to make it work, and let me know what you find. Mr. Reitz 65. KHonda says:$latex\frac{x}{\sqrt[6]{x+3}$• KHonda says:$latex\frac{x}{\sqrt[6] x+3}$• KHonda says: $\frac{x}{\sqrt[6]{x+3}$ 66. KHonda says: $\frac{x}{\sqrt[6] x+3}$ 67. KHonda says: $\intfrac{x}{\sqrt[6] x+3}$ • KHonda says: $\int frac{x}{\sqrt[6] x+3}$ • Jonas Reitz says: You’re close! Just add a backslash “\” before the word “frac”. Mr. Reitz (ps. I’m not sure how to solve this problem!) 68. Antonio Downer Math 1575-6638 $\int\frac{\sqrt{4x^2+1}}{8x} dx$ • Jonas Reitz says: Hi Antonio — I think the $8x$ should be on the top, not the bottom (unless I’m missing something). Try it out, and let me know. Mr. Reitz • Your correct, my mistake. $\frac{8x}{\sqrt {4x^2 +1}} dx$ • Oops.. $\int \frac{8x}{\sqrt {4x^2 +1}} dx$ 69. avald1046 says: $\int y^2 \cos (y^3) dy$ • Jonas Reitz says: Good! • u= $y^3$ du= $3y^2 dy$ dy= du/3y^2 int\ y^2cos(u)* (1/3y^2)du int\ cos(u)/3 du the integral of cos(u) is sin(u) => sin(u)/3 replace: u=y^3 answer:$latex \frac{sin y^3}{3}

• $\frac{sin y^3}{3}$

70. danytrueman says:

$late\int(1-t)(2+t^2)dt$

• Jonas Reitz says:

Just add the letter x to latex, and a space after the x — then it should work.

71. KHonda says:

$\int \frac{x}{\sqrt[4] x+3}} dx$

• KHonda says:

$\int \frac{x}{\sqrt[4] x+3} dx$

• Jonas Reitz says:

Looks nice! BUT I don’t know how to solve it… Try to find a solution, and if it doesn’t work out try modifying the problem.

72. $latex\int\ 2x(x^2+4)^{100}$

• $\int\ 2x(x^2+4)^{100}$

• $\int\ 2x(x^2+4)^{100} dx$

• Karen L. says:

$u = {x^2 + 4}$
$du = {2x}dx$

plug in:
$\int {u^{100}} du$
$= \frac{1}{101} {u^{101}} + c$
$= \frac{1}{101} {({x^2 +4})^{101}} + c$

• Jonas Reitz says:

Looks good!

73. andy21 says:

$\int x^2 e^(x^3+7) dx$

• andy21 says:

^ -Mahendra Seepersaud MAT1575-6637

• Jonas Reitz says:

Hi Mahendra — good problem! Just change the parentheses ( ) to curly brackets { }. That will put the entire expression $x^3+7$ into the exponent.

74. Drake says:

$\int_0^{\1} \x^2 (1 + 2x^3) ^ 5 dx$

75. Karen L. says:

$\int_4^{16} \frac{90x^2}{\sqrt{15x^3 + 5}} dx$

76. george says:

$\int_0^{4}\ x^ \frac{1}{2} dx$

77. Tiff Ca$e says: $/int_x{\2} \frac{3}{t+2} dt$ 78. Tiff Ca$e says:

$\int_2^{\x} \frac{3}{t+2}dt$

79. Tiff Ca$e says: $\int_2^{\x} \frac{3}{x+2} dx$ • Jonas Reitz says: Hi Tiff — you’re close! Get rid of the backslash in front of the x, and it should display properly. Quick question: is this a “find the derivative” problem? If so, convert the x’s (except the first one) to t’s, and add the instructions “find the derivative”. 80. pchen says: $\int_0^5 \sin x + cos x dx$ • Jonas Reitz says: Looks fine. • Drake says: Drake Li Section 6638 The answer will be the following : 1 + sin (5) – cos (5) 1 + ~-.96 – ~.28 ANS : .24 81. aman1992 says: $\int ex dx$ • aman1992 says: this one is real.. $\int xe^6x dx$ • aman1992 says: $\int xe^(6x) dx$ • aman1992 says: $\int xe^6x dx$ • Jonas Reitz says: Hi aman – just put the 6x into curly brackets { } to make them both appear in the exponent. However, if we do this, I don’t know how to solve the problem! See if you can solve it, or make a change. 82. lboruch says: $\int_{\pi}^{2\pi} \-cosx-2sinxdx$ 83. alamin163 says: Find the area between y=x^2 and y=x^3 between x=0 and x=1 when the function is given: &latex \int (x^2 – x^3) dx$

• alamin163 says:

$\int (x^2 – x^3) dx$

• Jonas Reitz says:

Weird – your formula should work, but doesn’t. After investigating, it seems that the minus sign in the middle is not a standard “dash”, but is a slightly longer dash character. Try deleting it, and typing it in again.

84. A company produces \int_\frac{x^2}{\sqrt{X}} solar panels an hour. How many panels will be made in six hours?

• Jonas Reitz says:

You’re off to a good start, but the question needs a bit of modification — I’m not sure how to solve it from the information given! For notation, don’t forget to include the “$latex” at the start, and “$” at the end.

85. Drake says:

Drake Li Section 6638

$\int_0^{\pi} \csc x + sec x dx$

• Jonas Reitz says:

Drake – the notation looks good! BUT the problem has problems — I’m not sure how to find the antiderivative of cscx or secx. In addition, there are places between 0 and pi where these functions are not defined (for example, secx = 1/cosx, which is undefined when sinx equals 0).

• Drake says:

$\int 2x(x^2 + 3)^4 dx$

86. darklor7 says:

Alexander Barbaran 7216

$\int_0^{3\frac\pi} \frac \sqr{x+3} \sqr{x-6}$

• darklor7 says:

it doesn’t work if i use \int 0^{3\pi} \frac \sqr{x+3} \sqr[3]{x-6}

• Jonas Reitz says:

Hi darklor7 – you’re on the right track! You need to put an underscore “_” before the zero to make it show up as the lower bound of integration. The code for the radical sign is \sqrt, not \sqr (don’t forget the t). Finally, after \frac, the numerator and denominator should each be enclosed in curly brackets { }, so it would start like this: “\frac{\sqrt{x+3} …” and so on. Give this a try and see if you can make it work.
-Mr. Reitz

87. prosenjitdas says:

∫ X^2+4x dx

• Jonas Reitz says:

Hi Prosenjit — the problem is fine, but you need to put it into latex so that the notation displays correctly! See if you fix it and re-post.
Thanks,
Mr. Reitz

88. jesus22 says:

a problem that I always didn’t know how to solve but one we took the test i lean how to solve it

$latex\int_0^{5}{\frac{\sqrt[3]{27}}{\sqrt[3]{{(x-3)}^4}}}dx$

• jesus22 says:

latex\int_0^{5}{\frac{\sqrt[3]{27}}{\sqrt[3]{{(x-3)}^4}}}dx

• jesus22 says:

$latex\int_0^{5}{\frac{\sqrt[3]{27}}{\sqrt[3]{{(x-3)}^4}}}dx$

• jesus22 says:

$latex\int_0^{5}{\frac{\sqrt[3]{27}}{\sqrt[3]{{(x-3)}^4}}}dx$

• jesus22 says:

$latex \int_0^{5}{\frac{\sqrt[3]{27}}{\sqrt[3]{{(x-3)}^4}}}dx$

• jesus22 says:

$\int_0^{5}{\frac{\sqrt[3]{27}}{\sqrt[3]{{(x-3)}^4}}}dx$