MAT 1221 Survey of Calculus Section 7.1 Integration by Parts

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Presentation transcript:

MAT 1221 Survey of Calculus Section 7.1 Integration by Parts

Expectations Show all the steps Simplify the answer. 7 minutes

Preview The reverse of the product rule

Derivatives and Antiderivatives

Product Rule

Definition of Antiderivatives

By Definition of Antiderivatives

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

Alternative Form

Integration By Parts

Example 1

Remarks

2. If we make a different choice such as

Example 2

Example 3

Additional Formula To make calculations a bit easier, we are going to adopt the following new formula

Example 4

Remarks Do not use IBP for all integrals. Sometimes, Substitution is easier.

Example 5

Next Class Session Learn how to use a CAS (Computer Algebra System) - Maple

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