If `f(x)` is a function defined `AA x in R` and `f(x) + f(-x) = 0 AA x in [-(T)/(2), T/2]` and has period T, then prove that `phi(X) =int _(a)^(x) f(t)` dt is also periodic with period T.

It is known that f(x) is an odd function in the interval [-(p)/(2),(p)/(2)] and has a period p, Prove that int_(a)^(x)f(t)dt is also periodic function with the same period.

If f(x) is a periodic function with period T, then

It is known that f(x) is an odd function and has a period p . Prove that int_(a)^(x)f(1)dt is also periodic function with the same period.

If f(x) is periodic function with period, T, then

If f(-x)+f(x)=0 then int_(a)^(x)f(t)dt is

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is

if f(x) is an odd periodic function defined on interval [-T/2,T/2], where T is the time period of f(x). Then time period of phi(x)=int_(a)^(x)f(x)dx is

If f (x) is periodic function with period T, then the function f (ax+b) where a gt 0, is periodic with period

Statement -1: If f(x + a)f(x-a) = - 1 for some positive constant 'a' and for all value of x in R, then f (x) is periodic function with period equal to 4a.Statement - 2 : If f(x+T) = f(x), AA x in R and for some positive constant T, then f(x) is periodic function with period equal to T.