# $\int_{0}^{\infty} f(x) \sin(x) dx$ from Complex Fourier Transform for $f(x)$ even

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?