No need to show any other work, can you just show how we got the 1/8 circled in blue ? What steps did we take to get that 1/8. I thought we only took 1/2 out and it confused me. 1+8.3.25sin? x cos x dxCos 2.x1+ cos 2x(1-cos² 2x)(1+ cos 2x) dx8.dxCOScos 2x- cos 2a - cos 2x da =1+ cos 4x1.CoS 2x dx =1+cos 2xCOS1+ cos 2x3COs 4x dx-sin 2xsin 4x(1-sin2 2x) cos 2x d.x. To compute this last integral,8.2.(1-sin 2x) cos 2x da16%3D1664we let u = sin 2x, so that du = 2 cos 2x dx. Then%3Dsin3 2xJa-|(1- sin 2r) cos 2x da1(1-u²) du:+Csin 2x+C.3.Thus, our original given integral is equal tosin 2x+C.3sin 2x)sin 2xsin 4.xsin 4x+C =16sin 2x%3D-1616648.6448

Answered: Image /qna-images/answer/98b00e30-c6af-4a76-ae37-440d63ad066d.jpg

1- cos 2x 2 1+ cos 2x 1 (1- cos? 2x)(1+cos 2x) dx = 8. 8.3.25 sin2 z cos a dx = 1+ 8 dx = cos 2x - cos 2x - cos 2x da = 1+ cos 2x - 8. sin 2x 1+ cos 4.x cos 2x dx = 8. + cos 2x - Cos 4x dx - 1 (1- sin 2r) cos 2x dr = 8 sin 4x 1 (1-sin2 2x) cos 2x d.x. To compute this last integral, 8. 16 64 we let u = sin 2x, so that du = 2 cos 2x dx. Then 16 sin 2x fa- 1 (1 - u?) du = u3 +C = 1 sin 2x - sin 2x) cos 2x dx = +C. 3 Thus, our original given integral is equal to sin 2x + C. sin 2r sin 4.x sin° 2x sin 4x sin 2x – 3 +C = 16 16 16 64 8. 64 48

1- cos 2x 2 1+ cos 2x 1 (1- cos? 2x)(1+cos 2x) dx = 8. 8.3.25 sin2 z cos a dx = 1+ 8 dx = cos 2x - cos 2x - cos 2x da = 1+ cos 2x - 8. sin 2x 1+ cos 4.x cos 2x dx = 8. + cos 2x - Cos 4x dx - 1 (1- sin 2r) cos 2x dr = 8 sin 4x 1 (1-sin2 2x) cos 2x d.x. To compute this last integral, 8. 16 64 we let u = sin 2x, so that du = 2 cos 2x dx. Then 16 sin 2x fa- 1 (1 - u?) du = u3 +C = 1 sin 2x - sin 2x) cos 2x dx = +C. 3 Thus, our original given integral is equal to sin 2x + C. sin 2r sin 4.x sin° 2x sin 4x sin 2x – 3 +C = 16 16 16 64 8. 64 48

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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No need to show any other work, can you just show how we got the 1/8 circled in blue ? What steps did we take to get that 1/8. I thought we only took 1/2 out and it confused me.