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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

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

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