Question

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

Answer 1

`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`