Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 16: Integrals and Vector Fields - Section 16.1 - Line Integrals - Exercises 16.1 - Page 944: 37


$2 \pi a^3 \delta$

Work Step by Step

Given: $x^2+y^2=a^2$ and $I_z=\int_C (x^2+y^2) \delta ds=\int_C (a^2) \delta ds$ Thus, $I_z=a^2 \delta \int_C ds$ The circumference of the curve is given as: $\int_C ds =2 \pi a$; So, $I_z=2 \pi a^3 \delta$
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