How do you evaluate the definite integral #int sin^(5)x * cos^(20)x dx# from [0,pi/2]?

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How do you evaluate the definite integral #int sin^(5)x * cos^(20)x dx# from [0,pi/2]?

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Answer 1 · 2016-09-08T23:55:22

#1/21-2/23+1/25#

Explanation:

#int_0^(pi/2) sin^(5)x * cos^(20)x dx =int_0^(pi/2) (1-cos^2x)^2cos^20 x sin x dx#
#=int_0^(pi/2) (1-2cos^2x+cos^4x)cos^20 x sin xdx =#
#=int_0^(pi/2)(cos^20x-2cos^22 x+cos^24x)sinx dx =#
#=-1/21(0-1)+2/23(0-1)-1/25(0-1)=#
#=1/21-2/23+1/25#

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How do you evaluate the definite integral #int sin^(5)x * cos^(20)x dx# from [0,pi/2]?

1 Answer

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