# 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

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

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