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

Exercise

Calculate the integral

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

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