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 15.3 - Area by Double Integration - Exercises 15.3 - Page 887: 26

Answer

50

Work Step by Step

$\int ^1_0 \int ^{2y-y^2}_{y^2}100(y+1)dxdy $ =$\int ^1_0[100(y+1)x]^{2x-y^2}_{y^2}dy $ =$\int^1_0 100(y+1)(2y-2y^2)dy $ =$200 \int^1_0(y-y^3)dy $ =200[$\frac{y^2}{2}-\frac{y^4}{4}$] =200($\frac{1}{4}$) =50
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