If `f` is an odd function, show that: `int_-a^a f(sinx)/(f(cosx)+f(sin^2x))dx=0`

If f is an odd function and I=int_(-a)^(a)(f(sin x))/(f(cos x)+f (sin^(2)x))dx , then

If f is an odd function,then evaluate I=int_(-a)^(a)(f(sin x))/(f(cos x)+f(sin^(2)x))dx

If f(x) is an odd function, then the value of int_(-a)^(a)(f(sin x)/(f(cos x)+f(sin ^(2)x))) dx is equal to

If f is an integrable function, show that int_(-a)^a xf(x^2)dx=0

If f is an integrable function, show that int_(-a)^af(x^2)dx=2int_0^af(x^2)dx

Statement l If f satisfies f(x+y)=f(x)+f(y), AA x,y in R,then int_(-5) ^5 f(x)dx=0 Statement II: If f is an odd function, then int_(-a) ^a f(x) dx =0

Prove that int_-a^a f(x) dx=0 , where 'f' is an odd function. And, evaluate, int_-1^1 log[(2-x)/(2+x)] dx

If f is a differentiable function and 2f(sinx) + f(cosx)=x AA x in R then f'(x)=

Let f be an odd function then int_(-1)^(1) (|x| +f(x) cos x) dx is equal to