Monday 11 September class

Topics:

• More on the FTC and problems 16, 17, and 18 of the WeBWorK “FTC part 2” – see also the student questions on Piazza on these problems.

• Integration by substitution.

Here are the examples I discussed in class: I may post slideshows or complete solutions later if I have time

 

\int\cos^{3}(x)\sin(x)\textrm{d}x: here we take u(x) = \cos(x), so \textrm{d}u = -\sin(x)\textrm{d}x

The result is -\frac{\cos^{4}(x)}{4} +C

 

\int x^{2}\sqrt{x^{3}+5)\textrm{d}x: here we take u(x) = x^{3} + 5, so \textrm{d}u = 3x^{2}\textrm{d}x

The result is \frac{2}{9}\left(x^{3}+5\right)^{\frac{3}{2}} +C

 

\int\frac{2x+3}{x^{2}+3x}\textrm{d}x: here we take u(x) = x^{2}+3x, so \textrm{d}u = (2x+3)\textrm{d}x

The result is \ln\left|x^{2}+3x\right| +C

 

\displaystyle \int_{0}^{1} e^{-3x}\textrm{d}x: here we take u(x) = -3x, so \textrm{d}u = -3\textrm{d}x: also, don’t forget to change the limits of integration when you substitute!

The result is \frac{1}{3} - \frac{e^{-3}}{3}

 

Homework:

• Last reminder: make sure that you have done everything that is listed on the first day post! Most especially, make sure that your City Tech email address is in the User Information in WeBWorK. There are still a number of student who have not done this, and it means that if you send me an email from inside of WeBWorK I will not be able to reply to your email.

• Review and study the examples we discussed in class (listed above).

• Do the WeBWorK: some is due by 11 PM tomorrow, Tuesday, and please do not wait to the last minute! The homework on the Substitution method is not due until Sunday, but try to do at least 5 problems by tomorrow.

• Tomorrow is primary election day in NY, so if you are a registered voter check out the NYC Campaign Finance Board’s Voter Guide and don’t forget to vote!

I believe that I have corrected or fixed all of the links in the previous posts on this blog, but if you find a link in any post that is broken or leads to the wrong thing, please let me know!

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!

Here is my slideshow on how to use Piazza to best effect: MAT1375:1575-UsingPiazza-slideshow