# Parseval's theorem and Fourier Transform proof

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Ineedhelp0
TL;DR Summary
I am searching for a proof that the square of a function is equal to the sum of the square of its transform.
Given a function F(t)
$$F(t) = \int_{-\infty}^{\infty} C(\omega)cos(\omega t) d \omega + \int_{-\infty}^{\infty} S(\omega)sin(\omega t) d \omega$$
I am looking for a proof of the following:

$$\int_{-\infty}^{\infty} F^{2}(t) dt= 2\pi\int_{-\infty}^{\infty} (C^{2}(\omega) + S^{2}(\omega)) d \omega$$

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