Question

सिद्ध कीजिए की
`int_(0)^(pi) (x dx)/(1+ sin^(2) x) = pi^(2)/(2sqrt(2))`.

Answer 1

`2I=2pi*int_(0)^(pi//2)(dx)/((1+sin^(2)x))`.
Divide num. and denom. by `cos^(2)x` and put `tanx=t`.