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

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

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.

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

If f is an odd function, then evaluate I=int_(-a)^a(f(sinx)dx)/(f(cosx)+f(sin^2x))

If f is an odd function, then evaluate I=int_(-a)^a(f(sinx)dx)/(f(cosx)+f(sin^2x))

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

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

If f(x)=f(a+x) , then prove that the value of int_(a)^(a+t) f(x)dx is independent of a.