# [SOLVED]Anti-derivatives of the periodic functions

#### Cbarker1

##### Active member
Dear Everyone,

I do not know how to begin with the following problem:

Suppose that $f$ is $2\pi$-periodic and let $a$ be a fixed real number. Define $F(x)=\int_{a}^{x} f(t)dt$, for all $x$ .
Show that $F$ is $2\pi$-periodic if and only if $\int_{0}^{2\pi}f(t)dt=0$.

Thanks,
Cbarker1

Last edited:

#### topsquark

##### Well-known member
MHB Math Helper
...if and only if $\int_{0}^{2\pi}f(t)dt$.
if and only if $$\displaystyle \int_0^{2 \pi}f(t)~dt$$ is what?

-Dan