Evaluate 3 sin(x) cos(x) dx by four methods. (a) the substitution u = cos(x) 0-흑 cos2(x) + C O sin(x) cos(x) + C 0-흑 sin2(x) + c O cos(2x) + c O sin(2x) + c (b) the substitution u = sin(x) O2 cos(2x) + c 2 sin(2x) + C 0 흑 cos?(x) + C O2 sin(x) cos(x) + C 0 흑 sin2(x) + C (c) the identity sin(2x) = 2 sin(x) cos(x) ㅇ클 cos2(x) + C sin(x) cos(x) + C O 2 sin(2x) + C cos(2x) + C O - sin?(x) + C (d) integration by parts ㅇ cos2(x) + C ○으 Cos(2x) + C 2 sin(2x) + C 2 sin(x) cos(x) + C O sin?(x) + C
Evaluate 3 sin(x) cos(x) dx by four methods. (a) the substitution u = cos(x) 0-흑 cos2(x) + C O sin(x) cos(x) + C 0-흑 sin2(x) + c O cos(2x) + c O sin(2x) + c (b) the substitution u = sin(x) O2 cos(2x) + c 2 sin(2x) + C 0 흑 cos?(x) + C O2 sin(x) cos(x) + C 0 흑 sin2(x) + C (c) the identity sin(2x) = 2 sin(x) cos(x) ㅇ클 cos2(x) + C sin(x) cos(x) + C O 2 sin(2x) + C cos(2x) + C O - sin?(x) + C (d) integration by parts ㅇ cos2(x) + C ○으 Cos(2x) + C 2 sin(2x) + C 2 sin(x) cos(x) + C O sin?(x) + C
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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![Evaluate 3 sin(x) cos(x) dx by four methods.
(a) the substitution u = cos(x)
O - cos?(x) + c
* sin(x) cos(x) + C
0-흑 sin2(x) + C
흐 cos(2x) + C
)음 sin(2x) + C
(b) the substitution u = sin(x)
O cos(2x) + C
2 sin(2x) + C
0 흑 cos2(x) + C
cos²(x) +
O sin(x) cos(x) + C
ㅇ 흑 sin2(x) + C
(c) the identity sin(2x) = 2 sin(x) cos(x)
0 흑 cos?(x) + C
O - sin(x) cos(x) + C
- sin(2x) + C
O - cos(2x) + C
O -3 sin?(x) + C
(d) integration by parts
0 흑 Cos?(x) + C
O4 cos(2x) + C
O - sin(2x) + C
- sin(x) cos(x) + C
0 흑 sin2(x) + C
o sin°x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75f283d3-de35-45b9-8b29-4974a6ee8b37%2Ffd611678-1f14-48d9-9ddd-b6cd8daff23f%2Flsrexsf_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluate 3 sin(x) cos(x) dx by four methods.
(a) the substitution u = cos(x)
O - cos?(x) + c
* sin(x) cos(x) + C
0-흑 sin2(x) + C
흐 cos(2x) + C
)음 sin(2x) + C
(b) the substitution u = sin(x)
O cos(2x) + C
2 sin(2x) + C
0 흑 cos2(x) + C
cos²(x) +
O sin(x) cos(x) + C
ㅇ 흑 sin2(x) + C
(c) the identity sin(2x) = 2 sin(x) cos(x)
0 흑 cos?(x) + C
O - sin(x) cos(x) + C
- sin(2x) + C
O - cos(2x) + C
O -3 sin?(x) + C
(d) integration by parts
0 흑 Cos?(x) + C
O4 cos(2x) + C
O - sin(2x) + C
- sin(x) cos(x) + C
0 흑 sin2(x) + C
o sin°x)
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