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 prove that varphi(x)=int_a^xf(t)dt is an even function.

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

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.

If f(x) is an odd function of x, then show that, int_(-a)^(a)f(x)dx=0 .

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.

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.

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

Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then f(x) is an odd function f(x) is a one-one function f(x) is an onto function f(x) is an even function