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

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

View Full Document Right Arrow Icon
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)     
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern