Evaluate the following integral:`int_0^pixsin^3x\ dx`

Explanation

`int_0^pixsin^3x\ dx`

`=int_0^pi x sin^2sinxdx`

`=int_0^pi x(1-cos^2x)sinx dx ---(1)`

`=int_0^pi (pi-x)(1-cos^2(p-x)sin(pi-x))dx`

`=int_0^pi (pi-x)(1-cos^2x)sinx dx ----(2)`

Adding 1 and 2,

`2I=int_0^pix(1-cos^2x)sinxdx+int_0^pi(pi-x)(1-cos^2x)sinx dx`

`2I=int_0^pi(1-cos^2x)sinx dx ----(3)`
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