Calculus2.5 - Section 7.2 Integration by Parts d(u v u dv v...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 7.2: Integration by Parts
Background image of page 1

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

View Full DocumentRight Arrow Icon
uu v du d v v   () v dv d v  v dv u v u Integrating we get This is the integral version of the product rule!
Background image of page 2
sin x x dx ux sin dv x dx s () co x x cos sin x x x C    uu v du d v v   cos dx x vx
Background image of page 3

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

View Full DocumentRight Arrow Icon
Idea Let u be part that gets better when we take derivative For example: Let dv be part that we can integrate For example : , ,ln n x x x sin ,cos , x x x e
Background image of page 4
25 x x e dx 2 2 ux du x dx 5 5 1 5 x x dv e dx ve 2 5 1 5 x e x uu v du d v v   5 2 5 x e x dx
Background image of page 5

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

View Full DocumentRight Arrow Icon
2 5 5 12 55 xx x e xe dx ux du dx 5 5 1 5 x x dv e dx ve 5 5 5 2 11 5 5 x x x e x C dx e xe    5 2 5 5 5 5 2 x x x e C e e
Background image of page 6
3 sin( ) x x dx There is a simple way to keep track 3 2 3 6 6 0 x x x sin cos sin cos sin x x x x x + - + - 3 c () os x x 2 ( i 3 n ) s x x o 6 cs x x n 6 si C x  Derivatives Integrals
Background image of page 7

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

View Full DocumentRight Arrow Icon
3 cos x e x dx 3 3 3 x x ue du e dx cos sin dv x dx vx 3 sin x e x 3 sin 3 x ex x d uu v du d v v  
Background image of page 8
3 3 3 cos sin 3 sin x x x e x dx e x e x dx   3 sin 3 ( x ex 3 3 3 x x ue du e dx sin cos dv x dx vx 3 sin x 3 co () s x e x 3 cos 3 ) x x e dx 3 3 x 3 9 x e x dx
Background image of page 9

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

View Full DocumentRight Arrow Icon
33 3 sin 3 cos 9 x x x
Background image of page 10
Background image of page 11

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

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 10/27/2011 for the course MATH 1352 at Texas Tech.

Page1 / 13

Calculus2.5 - Section 7.2 Integration by Parts d(u v u dv v...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online