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

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

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

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx

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

Prove that int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx . Hence find int_(0)^((pi)/(2)) sin^(2) xdx

Prove that : int_(-a)^(a)f(x)dx =2 int_(a)^(0) f(x)dx, if f(x) is even funtion =0 , if f(x) is off fuction.