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What is the integral of #(sinx)^3 dx# from 0 to #pi/2#?

1 Answer

Aug 7, 2015

#2/3#

Explanation:

#int_0^(pi/2) sin^3x dx = int_0^(pi/2) (1-cos^2x)sin x dx#

#=int_0^(pi/2)(sin x -cos^2x sin x) dx#

#=(-cos x+1/3cos^3 x )|_0^(pi/2)#

#=(-0+1/3*0)-(-1+1/3)#

#=2/3#

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