Math 202 Lecture 8 - L'Hôpital's rule part 2 and intro to integration by parts

In today's lecture, we first go over a few homework problems regarding hyperbolic trig functions and their derivatives and integrals. We then wrap up our discussion on L'Hôpital's rule, where we do many more examples--in particular, examples that have varying powers that invite the help of logarithms and exponentials to deal with.

At the end of the class, we introduce a new integration technique, the reverse of the product rule--integration by parts. This technique allows us to integrate functions inaccessible by the basic rule and integration by substitution. We derive the formula for integration by parts and do one example. We shall refine the method and do more examples next time.

[georgesadler]

Professor Smith, thank you for solving homework problems at the beginning of this lecture, however at the 7:00 minute mark there is a small error. For the Hyperbolic Cosine square of x, you have the Hyperbolic Cosine square of x equal to (e^ x + e^-x)/2 instead of Hyperbolic Cosine square of x equal to ( (e^x + e^-x)/2)^2). Please correct this error in the video. Integration by Parts is a powerful integration technique in all levels of Mathematics. At the 34:00 minute mark, the camera takes about two minutes to turn. At the 59:00 minute mark, the camera also takes over two minutes to turn. Please check these items in the video.