Feb 2 - Integration by Parts

Yesterday most of classtime was dedicated to working on a volume worksheet - taking the same region, R, and creating a variety of solids.

Today, we learned the first of two new integration techniques for the week. It is called integration by parts and has the basic rule:

Integral of u*dv = u*v - Integral of v*du

It is based on the formula used for the product of functions (the Product Rule).

My thought process is that once I've decided that an integral can't be done by substitution, I'll try integration by parts. The first step for me is to determine "dv." Essentially, dv should be the "most complicated" part of the integral that I can integrate easily. "u" is whatever is leftover.

We worked several examples in class. Notes from class are below.
p1

p2