If `f(t)` is an odd function, then prove that `varphi(x)=int_a^xf(t)dt` is an even function.

If f(z) is an odd function, prove that, int_(a)^(x)f(z)dz is an even function.

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

It is known that f(x) is an odd function 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 an odd function then int_(-a)^(a)f(x) is equal to-

Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even function.

STATEMENT 1: int_a^xf(t)dt is an even function if f(x) is an odd function. STATEMENT 2: int_a^xf(t)dt is an odd function if f(x) is an even function.

Statement - I : If f(x) is an odd function, then f'(x) is an even function. Statement - II : If f'(x) is an even function, then f(x) is an odd function.

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an odd function, then

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an even function, then

If f(x) is periodic function of period t show that int_(a)^(a+t)f(x)dx is independent of a.