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

If f(x) = f(a+x) and int_(0)^(a) f(x) dx = k, "then" int _(0)^(na) f(x) dx is equal to

Prove that the equality int_(a)^(b) f(x) dx = int_(a)^(b) f(a + b - x) dx

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

Let int_(0)^(a) f(x)dx=lambda and int_(0)^(a) f(2a-x)dx=mu . Then, int_(0)^(2a) f(x) dx equal to

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. int _(0)^(1) f (x) dx =

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

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