I Wasn’t Going To Generalize This, But...

0:00 Introduction to the general problem
2:16 Is the numerator always 1?
3:02 Advanced math that will be used in this video
3:46 General formula. Introducing gamma function.
5:08 Derivation starts. Introducing beta function.
6:59 Lemma (relation between beta and gamma functions) and its proof.
8:58 Change of variables in double integral. Completing the proof of lemma.
12:19 Completing the derivation of the general formula.

Link to my previous integral video (areas when n = 2, 3, 4):    • Calculating Areas by Integration: Sim...  

I initially didn't plan to make this video, but my last videos on calculating areas by integration got quite popular during a short period of time, so here's the GENERALIZED version of that problem with generalized answer. During the derivation of the general formula, we will encounter some fascinating concepts such as beta function, gamma function, and multivariable calculus.

#integration #BetaFunction #GammaFunction #integrals #areas #IntegrationBySubstitution #AreaaIntegral #Jacobian

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