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: 25

Answer

43,329

Work Step by Step

We set up the integral as follows: $\int ^5_{-5} \int ^0_{-2}\frac{10,000e^y}{1+\frac{|e|}{2}}dydx $ =$10,000(1-e^{-2}\int ^5_{-5}\frac{dx}{1+\frac{|e|}{2}})$ =$10,000(1-e^{-2})[\int^0_{-5}\frac{dx}{1-\frac{x}{2}}+\int ^5_0 \frac{dx}{1+\frac{x}{2}}]$ =$10,000(1-e^{-2})[-2ln(1-\frac{x}{2})]^0_{-5}+10,000(1-e^{-2})[2ln(1+\frac{x}{2})]^5_0$ =$10,000(1-e^{-2})[2ln(1+\frac{5}{2})]+10,000(1-e^{-2})[2ln(1+\frac{5}{2})]$ =$40,000(1-e^{-2})ln(\frac{7}{2})$ Which is approximately equal to: $\approx 43,329$
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