please answer using the references given & do not use shortcut methods since it is integration by parts. skip if unsure. thank you so much! Evaluate the integrals through INTEGRATION BY PARTS (Sudv= uv- fvdu.)utilize trigonometric integrals and Integration by Trigonometric Substitution given as reference below.|-9+16*-dx1.16*sin x-dxcos6 x2.REFERENCE of trig integrals:sin" xdx , where mɛNand m is oddsplit off a factor of sin.x• express the rest of the factors in terms of cos x using sin? x=1– cos? x• use the substitution u = cos x, du = -sinxdxsin" xdx orcos" xdx, where mɛNand m is even• express sin"x= (sin² x)m/2• use the half-angle identityor cos"x=(cos²x}m/2cos² x=÷(1+c|+ cos 2.x) or sin² x= ÷(1- cos2.x)REFERENCE cases for trig substitution:Case 1. Væ² – ư :· let u= asin0, so va² – ư² = acos0Case 2. Vư – a² =let u= asec0, so vư – á? = atan0Case 3. va? + ư² =let u= atan0, so va² + ư? = asec0

Answered: Image /qna-images/answer/25540b82-1888-4485-8575-52061692fef6.jpg

Evaluate the integrals through INTEGRATION BY PARTS (Sudv= uv- ſ vdu.) utilize trigonometric integrals and Integration by Trigonometric Substitution given as reference below. V-9+16* dx 1. 16* sin x -d.x cos6 x 2.

Evaluate the integrals through INTEGRATION BY PARTS (Sudv= uv- ſ vdu.) utilize trigonometric integrals and Integration by Trigonometric Substitution given as reference below. V-9+16* dx 1. 16* sin x -d.x cos6 x 2.

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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Question

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please answer using the references given & do not use shortcut methods since it is integration by parts. skip if unsure. thank you so much!

Evaluate the integrals through INTEGRATION BY PARTS (Sudv= uv- fvdu.)
utilize trigonometric integrals and Integration by Trigonometric Substitution given as reference below.
|-9+16*
-dx
1.
16*
sin x
-dx
cos6 x
2.
REFERENCE of trig integrals:
sin" xdx , where mɛNand m is odd
split off a factor of sin.x
• express the rest of the factors in terms of cos x using sin? x=1– cos? x
• use the substitution u = cos x, du = -sinxdx
sin" xdx or
cos" xdx, where mɛNand m is even
• express sin"x= (sin² x)m/2
• use the half-angle identity
or cos"x=(cos²x}m/2
cos² x=÷(1+c
|+ cos 2.x) or sin² x= ÷(1- cos2.x)
REFERENCE cases for trig substitution:
Case 1. Væ² – ư :
· let u= asin0, so va² – ư² = acos0
Case 2. Vư – a² =let u= asec0, so vư – á? = atan0
Case 3. va? + ư² =let u= atan0, so va² + ư? = asec0

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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