Prove that `int_-2^2 f(x^4)dx=2int_0^2 f(x^4)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

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

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

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

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

int_(-1)^2 (x/4+1/2)dx-int_-1^2x^2/4 dx

int_(-1)^2 (x/4+1/2)dx-int_-1^2x^2/4 dx