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

int_(0)^(a)f(x)dx

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

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

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

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

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

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

int_(m)^(0)f(x)dx is