`int_(0)^(1)(x^(2))/(1+x^(6))dx` का मान ज्ञात कीजिए ।

Explanation

माना `x^(3)=t`
`rArr" "3x^(2)dx=dt`
`rArr" "x^(2)dx=(dt)/(3)`
`x = 0" पर " t=0^(3)=0`
`x=1" पर "t=1^(3)=1`
`therefore int_(0)^(1)(x^(2))/(1+x^(6))dx=int_(0)^(1)(dt)/(3(1+t^(2)))`
`=(1)/(3)[tan^(-1)t]_(0)^(1)=(1)/(3)[tan^(-1)1-tan^(-1)0]`
`=(1)/(3)((pi)/(4)-0)=(pi)/(12)`