Evaluate the integrals through INTEGRATION BY PARTS only (Sudv=uv- fvdu.) Apply trigonometric integrals and Integration by Trigonometric Substitution. |-9+ 16* -dx 1. 16* 2. arctan(Vx – 2)dx sin x cos® x 3. -dx use this REFERENCE of trig integrals: | sin" xdx, where meNand m is odd • split off a factor of sinx • express the rest of the factors in terms of cos.x using sin? x = 1- cos² x • use the substitution u = cos.x, du=-sin.xdx • | sinx dx= - cos.x+ C • | cosx dx= sin.x+ C sin"xdx or cos" xdx, where meNand mis even • S sin° x dx= [a - 1 1 cos2x) dx= -x- sin2x+ C 2 4 • express sin"x= (sin² x)m/2 or cos" x= (cos²x)m/2 • use the half-angle identity | cos? x dx = (1+ cos 2.x) dx=-x+ sin2.x+C 1 %3D 1

Evaluate the integrals through INTEGRATION BY PARTS only (Sudv=uv- fvdu.) Apply trigonometric integrals and Integration by Trigonometric Substitution. |-9+ 16* -dx 1. 16* 2. arctan(Vx – 2)dx sin x cos® x 3. -dx use this REFERENCE of trig integrals: | sin" xdx, where meNand m is odd • split off a factor of sinx • express the rest of the factors in terms of cos.x using sin? x = 1- cos² x • use the substitution u = cos.x, du=-sin.xdx • | sinx dx= - cos.x+ C • | cosx dx= sin.x+ C sin"xdx or cos" xdx, where meNand mis even • S sin° x dx= [a - 1 1 cos2x) dx= -x- sin2x+ C 2 4 • express sin"x= (sin² x)m/2 or cos" x= (cos²x)m/2 • use the half-angle identity | cos? x dx = (1+ cos 2.x) dx=-x+ sin2.x+C 1 %3D 1

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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