Prove that `int_0^(2a) f(x)/(f(x)+f(2a-x))dx=a`

Prove that: int_a^b(f(x))/(f(x)+f(a+b-x))dx=(b-a)/2

The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to

Prove that: int_0^(2a)f(x)dx=int_0^(2a)f(2a-x)dxdot

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

If f(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

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

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f is an integrable function such that f(2a-x)=f(x), then prove that int_0^(2a)f(x)dx=2int_0^af(x)dx