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Spherical and Cylindrical Coordinates – Between a sphere and a cone – Exercise 4619

Exercise

Calculate the integral

\int_0^1 dx\int_0^{\sqrt{1-x^2}} dy\int_{\sqrt{x^2+y^2}}^{2-x^2-y^2} z^2 dz

Final Answer


\int_0^1 dx\int_0^{\sqrt{1-x^2}} dy\int_{\sqrt{x^2+y^2}}^{2-x^2-y^2} z^2 dz=\frac{\pi(2\sqrt{2}-1)}{15}

Solution

Coming soon…

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