where did the pi go? area of a superellipse

Published: 26 May 2022
on channel: Dr Peyam

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calculating the area of a super ellipse. Here we find the area enclosed by a pseudo ellipse, which is a generalization of an ellipse but with n. Special cases include squares, circles, and ellipses. After a change of variables, we transform this geometric figure into an integral, which involves the beta function and which has been calculated previously using the Laplace transform. The answer includes the gamma function and factorials, but where did the pi go? This is a must see for calculus and math students, enjoy!

Laplace integral:    • Laplace integral gone BANANAS 🍌

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