My book presents the following simplification: $$A(w) = \frac{1}{\pi}\int_{-\infty}^{\infty} e^{-kx}cos(wx)dx = \frac{2}{\pi}\int_{0}^{\infty} e^{-kx}cos(wx)dx$$ But I can't understand why, since exponentials are neither odd nor even functions. There's something I'm missing ?
2026-03-30 10:53:17.1774867997
Is exponential even?
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I doubt this is true. I don't think the first integral converges.