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

Explanation

माना `sinx=t`
`rArr" "cos xdx=dt`
`{:(x=0 ," पर ",t=sin0=0),(x=(pi)/(2)," पर ",t=sin.(pi)/(2)=1):}`
`therefore int_(0)^(pi//2)(cosx)/(1+sinx^(2)x)dx=int_(0)^(1)(dt)/(1+t^(2))`
`=[tan^(-1)t]_(0)^(1)=tan^(-1)1-tan^(-1)0=(pi)/(4)`