A famous exercise which one encounters while doing Complex Analysis (Residue theory) is to prove that the given integral:

∫∞0sinxx dx=π2
Well, can anyone prove this without using Residue theory. I actually thought of doing this:

∫∞0sinxx dx=limt→∞∫t01t(t−t33!+t55!+⋯) dt
but I don't see how π comes here, since we need the answer to be equal to π2 .

A

**NSWER:-**

**Here's another way of finishing off Derek's argument. He proves**

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