Assignment (due at start of class on Monday, September 23) . 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:
- It can be from anything we have studied in the first six classes of the semester (up through Section 3.3, Trigonometric Substitution).
- 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 WeBWorK assignments, the textbook, my lecture notes, 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 is the meaning of the following notation?”. Bonus points for creative questions!
- 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. Only one solution per person, please (and only one correct solution for each problem).
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: $\int x^2 dx$then (after you post the comment) you should see this:
Here is an integral: $\int x^2 dx$
Each equation or expression begins and ends with a dollar sign. In between, 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. | $\int_0^{\pi} \sin x dx$ | $\int_0^{\pi} \sin x dx$ |
| B. | $\frac{x+1}{x^2 + 5x}$ | $\frac{x+1}{x^2 + 5x}$ |
| C. | $\sqrt{x+1} + \sqrt[5]{x+6}$ | $\sqrt{x+1} + \sqrt[5]{x+6}$ |
Some notes about these examples:
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 here 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.
If 14 ≤ f(x) ≤16, then
….. ≤ $\int_3^{\8} \f(x) dx ….. ≤
Hi Nicholas, Thanks for being first to give this a try! You’re off to a great start – a few suggestions: you’re missing a dollar sign at the end of your integral (after dx), and you have one or two unneeded backslash characters (before the 8 and before the f(x). You can edit your comment, or leave a new one, if you want to try again. Best of luck!
Thanks, prof. was just trying it out to see what I could come up with.
No worries – feel free to keep experimenting 🙂
If 14 ≤ f(x) ≤16, then
….. ≤ $\int_3^{\8} \f(x) dx$ ….. ≤
TAKE 2
Great improvement! I would remove the backslash “\” before 8 and before f(x).
If 14 ≤ f(x) ≤16, then
….. ≤ $int_3^{8} f(x) dx$ ….. ≤
If 14 ≤ f(x) ≤16, then
….. ≤ $\int_3^{8} f(x)dx$ ….. ≤
Awesome – your final submission (the comment following this one) looks perfect. Great work troubleshooting!
$\int (cosx)^4 (sinx)^3 dx$
Looks good! We’ll be talking about problems like this today in class 🙂
if 10<= g(x)<=12, then <= anti derivative 2 to 6 g(x) dx….<=
That is actually the problem I propose is :
$int cos^4 x sin^3 x dx$
$\fract{cos^5 x}{5} – \fract{cos^7 x}{7} + c$
Hi Mariame! To fix your fraction – just remove the letter “t” so it looks like \frac{}{} instead of \fract{}{}.
$\frac{(cos^5)x{5} – \frac{(cos^7)x}{7}$
Very close – I think you’re just missing a closing curly bracket after {(cos^5)x
$\int_0^{\pi}\6*cos^2 x -\sin x dx$
$\int_0^{\pi} 6\cos^2 x -\sin xdx$
Looks great!
Hey Gabriel
Is the answer of the problem $3pi – 2$ ?
$\int x^2 \lnx dx$
Great! – add a space into \ln x and it should render correctly.
.
Hi Louis – looks like you tried to post an image, but it didn’t come through. Try writing the your problem in text and see how it comes out!
$int cos^4 x sin^3 x dx$
$\int tan^6 x sec^4 x dx $
Looks great!
$\int 2x^2 * \sqrt{x+4}dx$
Great job!
$\int$\frac{1}{x^2+4}dx$
$\intfrac{1}{x^2+4}dx$
$\int $\frac{1}{x^2 + 4} dx$
$\int \frac{1}{x^2 + 4} \, dx$
Great work and good persistence!
$\int x^2 e^x dx$
Use Intergration by Parts to evaluate the integral.
$\int x^2 e^2x dx$
$\int x^4 ln(x) dx$
Answer: $\frac{x^5 \ln(x)}{5} – \frac{x^5}{25} + C$
Looks good!
∫x^(6) cos (8x^(3))dx
Tricky – I like it!
$\int \frac{1}{\sqrt{9 – x^2}} \, dx$
Great!
$\\ x ln x dx$
I computed the answer to be:
1/2*x^2*ln(x)-{x^2/4}+C
Good! If you add “\int” instead of “\\” at the beginning you’ll get an integral sign
int sqrt(x^(4)+6)*8x dx
Good! To get it render as math, put a dollar sign at the beginning and end of the whole expression, and add a backslash before “int” to get an integral sign.
$\int \frac{dx}{\sqrt{9 – x^2}}
Looks good – just missing a dollar sign at the end, I think
$int\frac{12x}{16x}{(6x^2)^2}dx$
A correction:
$\int \frac{12x}{16x+(6x^2)^2}dx$
Great! Tricky one 🙂
$\int /frac{x^5+55}{x-19}$
$ \int /frac {x^5+55} {x-19} $
$/frac{x^5+55}{x-19}$
$\int\frac{x^5+55}{x-19}$
From integral of 4 to 9. 4x^2+3/(sqrt 3)dx
Integral of 7xsin(-5x)dx
Let g(x) integral from 2 to x 7t^2 dt. Find g’(x).
$\4x sin 3x^2 dx$
-2/3cos(3x)^2 +C
$\int 3x((x^2)-5) dx$
$\int x^2(x-3)^7 dx$
∫e^2x cos(5x)dx
$\int cos^5 x dx$
If f(x) = integral from x to 10 t^3 dt. What is f'(x) and f'(2)
this is my exam proble
Hi Simon – it looks like you tried to post an image, but it didn’t come through. Try writing the your problem in text (as described in the assignment above) and submit it again. Thanks
NOTE: Private response is visible only to instructors and to the post’s author.
∫(sin^2x)/(1+cos^2x)dx
anti deritative x^3+25/(sin(2x))
∫(sin^2x)/(1+cos^2x)dx
This is me retyping the picture I had before