This question was inspired by this question:
Evaluating the integral ∫∞0sinxx dx=π2?
Well, can anyone prove this without using Residue theory. I actually thought of doing this:
∫∞0sinxxdx=limt→∞∫t01t(t−t33!+t55!+⋯)dt
but I don't see how \pi comes here, since we need the answer to be equal to \frac{\pi}{2}.
Answers were given to the stated question -- how to prove without using Residue theory. Yet the quote suggests an obvious follow-up question: can you prove the integral from the Taylor series expansion directly, somehow?
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