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I am able to calculate $\int_{0}^{\infty} f(x) cos(x) dx$ for $f(x)$ being even by taking the real part of Complex Fourier transform (at $\omega = 1$). The two-sided sine transform is $0$, as $f(x)$ is even.

Is there a way to calculate the one-sided integral $\int_{0}^{\infty} f(x) sin(x) dx$ from the complex fourier transform $\int_{-\infty}^{\infty} f(x) e^{i \omega x} dx$ when f(x) is even?

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