`int_(0)^(pi//2) sin^(3)xdx` का मान ज्ञात कीजिए।

Explanation

`int_(0)^(pi//2)sin^(3)xdx`
`=int_(0)^(pi//2)(3sinx-sin3x)/(4)dx`
`=(1)/(4)[-3cosx+(1)/(3)cos3x]_(0)^(pi//2)`
`=(1)/(4)[-3cos.(pi)/(2)+(1)/(3)cos.(3pi)/(2)]-(1)/(4)[-3 cos 0+(1)/(3)cos0]`
`=0-(1)/(4)(-3+(1)/(3)=(2)/(3))`