chap7sec1

# chap7sec1 - cos x a x x dx b xe dx HINTS 1 You must be able...

This preview shows pages 1–2. Sign up to view the full content.

7.1 Integration by Parts Review the integrals shown on page 469 and integration by substitution. Examples:    1 ( ) ( ) (sin )(cos ) x x e e a dx b x x dx + Remember - integration is done by various techniques and is not as straightforward as differentiation. Typically, selecting the proper technique is the most difficult aspect of integration. Large numbers of practice problems is the best solution to the difficulty you may encounter. The integration rule that corresponds to the product rule for differentiation is integration by parts. INTEGRATION BY PARTS.     u dv uv v du = - OBJECT:  select a substitution that yields a  simpler  integral. GENERALLY:  select u = f(x) to be a function that becomes simpler when differentiated (or at least not more  complicated). Examples (Note Example 2 on page 471)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( ) cos ( ) x a x x dx b xe dx HINTS: 1. You must be able to integrate dv. It will often be the most complicated part that fits an integration formula. 2. An application of the formula should produce an integral that is easier (or at least no harder) to integrate. 3. , 0, let and p kx p kx x e dx p u x dv e dx = = 4. (ln ) , 0, let (ln ) and p q q p x x dx p u x dv x dx = = Integration by parts may need to be applied more than once. Note example 3 on page 471. Examples 2 2 3 ( ) sin 2 Requires integration by parts twice. ( ) Think ahead on this one. ( ) sin(ln ) Refer to example 4. ( ) Area bounded by 5ln , ln( ) ( ) Volume using shells from rotati x a x x dx b x e dx c x dx d y x y x x e = = ng about the y-axis , , . : 1 x x y e y e x-= = =...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern