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.

Prove that the derivative of and odd function is an even function.

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

If f(x) is an odd function then int_(-a)^(a)f(x) is equal to-

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

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

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 G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

Let f(x) be a differentiable even function, consider the following statements : (i) f'(x) is an even function. (ii) f'(x) is an odd function. (iii) f'(x) may be even or odd. Which of the above statements is/are correct ?