Complex Analysis: A Trigonometric Integral

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Today, we evaluate the integral of 1/(1+sin^2(x)) from 0 to 2pi by redefining it in terms of complex exponential functions, then using the residue theorem reach the final answer.
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Комментарии
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I am a 14 year old trying to self teach myself, and I can easily understand your explanations. Your channel is criminally underrated! You deserve at least 100K imo

polychromaa
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Vraiment c est super
Je sais pas comment je peux remercier

LatifaEssa
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Thanks for you videos.

You dont need to Del'hospital if you factor the polynomial with the roots you found.

ΜιχαήλΣάπκας
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Of course I enjoyed.
Thank you so much dear *QN³*

wuyqrbt
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Awesome content, I love the clear explanations. Keep up the good work mate, it is good to see that you are getting ads from youtube! Also, good job with your ATAR, are you pursuing mathematics at university? I am at ANU in physics!!

Jocularious
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fun fact:

gamma(1/4)*gamma(3/4) = sqrt(2)*pi

as well

xulq
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I have a doubt, why did you take e^iz as the primary variable in the sinx/x integral and not here?

flix
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Dear *QN³*
Please make a video about especial function *Ei(z)* ( actually I mean:
Integral e^(-x)/x ).
We can solve it with complex analysis?!
Thank you so much

wuyqrbt
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We solve this in our jee practice, very easy

KingGaming-gwks