`int_(0)^(1)xe^(x^(2))dx`

Explanation

माना `int_(0)^(pi//2)cos^(2)x dx=int_(0)^(pi//2)((cos2x+1)/(2))dx`
`=(1)/(2)int_(0)^(pi//2)cos 2x dx +(1)/(2)int_(0)^(pi//2)1dx`
`=(1)/(2)[(sin 2x)/(2)]_(0)^(pi//2)+(1)/(2)[x]_(0)^(pi//2)`
`=(1)/(2)((sinpi)/(2)-(sin0)/(2))+((pi)/(2)-0)]=(pi)/(4)`