Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 17 - Line and Surface Integrals - 17.4 Parametrized Surfaces and Surface Integrals - Preliminary Questions - Page 957: 1

Answer

$\mathop \smallint \limits_{}^{} \mathop \smallint \limits_S^{} f\left( {x,y,z} \right){\rm{d}}S = 50$

Work Step by Step

The surface integral of a function $f\left( {x,y,z} \right)$ is given by $\mathop \smallint \limits_{}^{} \mathop \smallint \limits_S^{} f\left( {x,y,z} \right){\rm{d}}S$. Since $f\left( {x,y,z} \right) = 10$, so $\mathop \smallint \limits_{}^{} \mathop \smallint \limits_S^{} f\left( {x,y,z} \right){\rm{d}}S = 10\mathop \smallint \limits_{}^{} \mathop \smallint \limits_S^{} {\rm{d}}S = 10 \times 5 = 50$
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