Consinder the indefinite integral f sin³(x) dx a) Explain why the substitution u = sin(x) will not work. b) Using the Pythagorean identity sin² x + cos² x = 1 write sin³ x as the product of sin x and some other function.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
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3. Consinder the indefinite integral f sin³(x) dx
a) Explain why the substitution u = sin(x) will not work.
b) Using the Pythagorean identity sin?x + cos² x = 1 write sin³ x as the product of sin x and some other
function.
c) Now use u = cos x and evaluate the integral.
d) Use a similar approach to evaluate S cos³(x) dx
Transcribed Image Text:3. Consinder the indefinite integral f sin³(x) dx a) Explain why the substitution u = sin(x) will not work. b) Using the Pythagorean identity sin?x + cos² x = 1 write sin³ x as the product of sin x and some other function. c) Now use u = cos x and evaluate the integral. d) Use a similar approach to evaluate S cos³(x) dx
cos³ x
b. sin(x) (1 – cos² x)
S sin°(x) dx = os" I.
cos x + C
3
sin x
d. ſ cos³(x) dx = sin x – * + C
3
Transcribed Image Text:cos³ x b. sin(x) (1 – cos² x) S sin°(x) dx = os" I. cos x + C 3 sin x d. ſ cos³(x) dx = sin x – * + C 3
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