The value of the integral `int_0^(2a)[(f(x))/({f(x)+f(2a-x)})]dx "is equal to "a`

Evaluate int_(0)^(a)(f(x))/(f(x)+f(a-x)) dx.

If int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1 , then the value of the integral int_-1^1(f(x))dx is equal to

If f(x)=(2-xcosx)/(2+xcosx)andg(x)= "log"_(e)x, (xgt0) then the value of the integral int_(-pi//4)^(pi//4)g(f(x)) dx is

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

If int_(0)^(a) f(x) dx + int_(0)^(a) f(2a-x) dx =

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

By using the properties of definite integrals, evaluate the integrals Show that int_(0)^(a)f(x)g(x)dx=2int_(0)^(a)f(x)dx , if f and g are defined as f(x)=f(a-x) and g(x)+g(a-x)=4 .

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to