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

If f(t) is a continuous function defined on [a,b] such that f(t) is an odd function, then the function phi(x)=int_(a)^(x) f(t)dt

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

Given f an odd function periodic with period 2 continuous AA x in R and g(x)=int_0^x f(t)dt then (i) g(x) is an odd function (ii) g(x+2)=1 (iii) g(2)=0 (iv) g(x) is an even function

If f(x) is an odd function,then write whether f'(x) is even or odd.

If f(x) is an even function,then write whether f'(x) is even or odd.

The function L(x)=int_(1)^(x)(dt)/t satisfies the equation