Contour Integrating sin(x)/x

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We use Cauchy's Theorem to evaluate the integral of sin(x)/x from -∞ to ∞, first sketching an informal proof and then giving relevant rigorous details for advanced viewers.

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Hello again! Needless to say, it has been a while since the previous video! Thank you to everyone that is willing to check out the newest video after such a long wait. I will try to post more regularly for at least the next couple months. =)

LetsSolveMathProblems

I was trying to remember what your channel was called, and now you reminded me by posting a video! Good to see your work again

txikitofandango

Hey! Good seeing you back, also at 13:33 why are we only considering the real part of the exponent? I guess the imaginary part would just give another phase of magnitude 1? Not sure, thanks!

taccat

Yeah complex integration techniques it very fascinating; so you can deduce constant gamma from expanding contour integration of 1-cos(x) /x ; from 0 to infini ; and many more advanced méthode that could you found in famous complex book and one of my favorite book is written in middle 1889 from…

__hannibaal__

Hi, i do not quite understand why at minute 13:21 you don't consider exp(i\theta) and i no more, can anyone tell me why?

matteomoioli

Hey! I think you sound like someone I met at a grad school open house, curious if it was you.

irvingg

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