Thomas' Calculus 13th Edition

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

Chapter 15: Multiple Integrals - Section 15.8 - Substitutions in Multiple Integrals - Exercises 15.8 - Page 930: 5

Answer

2

Work Step by Step

$\int^4_0 \int^{(y/2)-1}_{y/2} (x-\frac{y}{2}) dx $ dy =$\int^4_0 [\frac{x^2}{2}-\frac{xy}{2}]^{\frac{-y}{2}+1}_{\frac{y}{2}}$ dy =$\frac{1}{2}\int^4_0 [(\frac{y}{2}+1)^2-(\frac{y}{2})^2-(\frac{y}{2}+1)y+(\frac{y}{2})]$ dy =$\frac{1}{2} \int^4_0 (y+1-y)dy $ =$\frac{1}{2} \int^4_0 dy $ =$\frac{1}{2}(4)=2$
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