Cylindrical and Spherical Coordinates — Cheat sheet

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Core rule

Cylindrical: $dV=r\,dr\,d\theta\,dz$ . Spherical with $\phi$ from $+z$ : $dV=\rho^2\sin\phi\,d\rho\,d\phi\,d\theta$ .

State the angle convention. Transform the solid, integrand and volume factor together.