— Lemma

MediumChange of variables

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #18 · Multivariable Calculus · Change of variables

From the limits of integration describe each region and find its volume. The inner integral has the inner limits.

$\int_{0}^{2 π} \int_{0}^{π /4} \int_{1}^{3} ρ^{2} sin ϕ d ρ d ϕ d θ$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #18

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