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Spherical and Cylindrical Coordinates – On an ellipse – Exercise 4620

Exercise

Calculate the integral

\int\int\int_T (\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}) dxdydz

Where T is bounded by the surfaces

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1

Final Answer


\int\int\int_T (\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}) dxdydz=\frac{4}{5}abc\pi

Solution

Coming soon…

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