MAT 1235 Calculus II Section 7 1 Integration

MAT 1235 Calculus II Section 7. 1 Integration By Parts http: //myhome. spu. edu/lauw

Homework and … l l Web. Assign 7. 1 (17 problems, 129 min. ) You are not helping yourself if you use Wolfram Alpha or other resources to cheat on your HW* (*2014 -2019)

Exam II l l Wednesday Time: 1: ? ? -2: 50

Exam II l l l Be sure to look at the quiz solutions. If you have questions, resolve them ASAP. Do not wait until the exam day to ask that question. Get help before it is too late. Exam II is coming up in 9 days. Exam II practice problems are online***

Preview l l l Finding antiderivatives are way-way more difficult than finding derivatives. We need to develop more techniques to help finding antiderivatives. IBP is considered as the reverse process of the product rule.

Product Rule

Product Rule

Definition of Antiderivatives

Rationale Easier Difficult The integral on the right hand side is easier to evaluate than the on the left hand side

Rationale Easier Difficult The integral on the right hand side is easier to evaluate than the on the left hand side

Alternative Form

Integration By Parts

Example 1

Example 1(Analysis) l

Example 1(Analysis) l

Example 1(Analysis) l

Example 1(Analysis) l

Example 1

Example 1 What if?

Example 1 What if?

Take Away Lesson l

Example 2

Expectations l l All supporting steps are required and done on the right side. The best practice is in this order!

Example 3

Example 4 (Classical Example)