Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 15 - Multiple Integrals - 15.7 Triple-Integrals in Cylindrical Coordinates - 15.7 Exercises - Page 1083: 13

Answer

Cylindrical coordinates: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}

Work Step by Step

Consider that $z-axis$ be the axis of the cylindrical shell whose center is at the origin. Conversion of rectangular to cylindrical coordinate system as follows: $r^2=x^2+y^2$ and $\tan \theta=\dfrac{y}{x}$, $z=z$ Now, the cylindrical coordinates inside the shell are: {$(r, \theta, z) \in E|6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,-10 \leq z \leq 10$} Our Cylindrical coordinates are : $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}
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