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[SOLVED] Anti-derivatives of the periodic functions

Cbarker1

Active member
Jan 8, 2013
255
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
Aug 30, 2012
1,180