7.1 Notes.pdf - 7.1 Integration by parts Math 142 Spring 2020 Chapter 7 Techniques of Integration Goals of this chapter \u2022 Develop methods for

# 7.1 Notes.pdf - 7.1 Integration by parts Math 142 Spring...

• 6

This preview shows page 1 - 3 out of 6 pages.

7.1 - Integration by parts Math 142 - Spring 2020 Chapter 7 - Techniques of Integration Goals of this chapter: Develop methods for integrating (i.e., finding antiderivatives for) more types of functions. (In addition to the substitution method.) 7.1 - Integration by parts Goals of this section: Apply the “integration by parts” method. Warmup/Motivation: Compute Z ln( x ) dx Today’s goal: 1 of 6 f C Not Correct Answer S dx in 4 to but it's not helpful We will know that In x x Incx xtc this is bk Hnk xtc E x'T th x l l INCH How can we come up w this answer Translate product race differentiation into integration by parts integration
7.1 - Integration by parts Math 142 - Spring 2020 Integration by Parts: Let u and v be functions of x (i.e., u = u ( x ) and v = v ( x )). Then by the product rule: Example 0: Compute Z ln( x ) dx Example 1: Compute Z x cos x dx When to use integration by parts: How to choose u and dv : 1. Choose dv so that 2. Choose u so that 2 of 6 Product Rule au u ddftu.dfou fudfatfvdf.ee fudai au Su do Formula For indefinite S udu uu Sudu integral Formula
• • • 