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

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

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.

Statement 1: If f(x) is an odd function,then f'(x) is an even function.Statement 2: If f'(x) is an even function,then f(x) is an odd function.

STATEMENT 1:int_(a)^(x)f(t)dt is an even function if f(x) is an odd function.STATEMENT 2:int_(a)^(x)f(t)dx is an odd function if f(x) is an even function.