`int_(0)^(1)(sin^(-1)x)/(sqrt(1-x^(2)))dx` का मान ज्ञात कीजिए ।

Explanation

माना `sin^(-1)x=t`
`rArr" "(1)/(sqrt(1-x^(2)))dx=dt`
अब `x=0" पर "t=sin^(-1)0=0`
`x=1" पर "t=sin^(-1)1=pi//2`
`therefore" "int_(0)^(1)(sin^(-1))/(sqrt(1-x^(2)))dx`
`" "=int_(0)^(pi//2)t dt=[(t^(2))/(2)]^(pi//2)`
`=(1)/(2)((pi)/(2))^(2)-0=(pi^(2))/(8)`