Answered: 2 (r2 cos? 0 + z2)r de dr dz 0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.4: Multiple-angle Formulas

Problem 54E

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Question

The integrals we have seen so far suggest that there are preferred
orders of integration for cylindrical coordinates, but other orders usually
work well and are occasionally easier to evaluate. Evaluate the
integrals

Expert Solution

Step 1

We have given

$\int_{0}^{1} \int_{0}^{\sqrt{z}} \int_{0}^{2 π} (r^{2} \cos^{2} θ + z^{2}) r d θ d r d z$

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