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I have super ellipse x^4+y^4=9592^4 inside a square with edges equal to 9592*2. I want to find out what the area is between the square and the super ellipse but the super ellipse math for area is a little beyond my abilities.

In reality I am trying to solve for the area between the two to equal 93,512 by only changing the power the super ellipse uses to be created. x^z+y^z=9592^z

Can this be done?

Joe
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1 Answers1

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Rearrange to get $y=(9252^4-x^4)^{\frac 1 4}$

Then integrate.

tomi
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    And how to integrate? –  Mar 15 '15 at 00:58
  • With help from wolfram: $$\int_0^{9252} \sqrt[4]{9252^4-x^4} , dx=\frac{42799752{} {\Gamma} \left(\frac{1}{4}\right) {\Gamma} \left(\frac{5}{4}\right)}{\sqrt{\pi }}$$ – Frieder Mar 15 '15 at 03:08