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

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Answer 1 · 2015-08-07T18:12:35

$2/3$

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

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

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

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

$=2/3$

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