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Can easily change OS settings Access settings that are hidden to you Check if the video card is workingQ: How to calculate the integral of an expression over the volume of a sphere? I have an expression of the form: $\iint \frac{\mathbf{1}}{4\pi\epsilon_0 c^2}\,dV$ Where $dV$ is the volume element over a sphere. How to calculate this using Fubini’s Theorem? Any hints? A: A brute force approach using cylindrical coordinates would be to do the following. Step 1: choose a coordinate system for the sphere that is compatible with your expression. For example, if $$\iint\frac{\mathbf1}{4\pi\epsilon_0 c^2}\,dV = \iint\frac{r^2\sin\theta\cos\theta\,d\theta\wedge d\phi}{4\pi\epsilon_0c^2} = \iint\frac{r^2\sin\theta\cos\theta\,dr\wedge d\theta}{4\pi\epsilon_0c^2}$$ then our choice of coordinates will be $r$ and $\theta$, as illustrated below: Step 2: compute the determinant of the transformation matrix. $$\mathrm{d}V = \big|\mathrm{d}r\wedge\mathrm{d}\theta\big| = \frac{r^2\sin\theta\cos\theta\,dr\wedge d\theta}{4\pi\epsilon_0c^2}$$ Step 3: invert the transformation matrix and integrate. \iint\frac{\mathbf1}{4\pi\epsilon_0 c^2}\,dV = \frac1{4\pi\epsilon_0c^2}\int_0^{2\pi}\int_0^\pi\frac{r^2\sin\theta\cos\theta\,dr\wedge d\theta}{4\pi\epsilon_0c^2} = \frac1{4\pi\epsilon_