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

The value of int_(-pi)^(pi) sinx f(cosx)dx is

Property 8: If f(x) is a continuous function defined on [-a; a] then int_(-a) ^a f(x) dx = int_0 ^a {f(x) + f(-x)} dx

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

Let f:[0,1]to R be a continuous function then the maximum value of int_(0)^(1)f(x).x^(2)dx-int_(0)^(1)x.(f(x))^(2)dx for all such function(s) is:

If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , then evaluate int_(sintheta)^(cos e ctheta)f(x)dx

If f(x) is a continuous function satisfying f(x)=f(2-x) , then the value of the integral I=int_(-3)^(3)f(1+x)ln ((2+x)/(2-x))dx is equal to

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

If int f(x)dx = F(x), f(x) is a continuous function,then int (f(x))/(F(x))dx equals

If f(0)=1,f(2)=3,f'(2)=5 ,then find the value of I_(1)=int_(0)^(1)xf''(2x)dx