Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 15 - Section 15.4 - Applications of Double Integrals - 15.4 Exercise - Page 1024: 1

Answer

The total charge on the rectangle $D$ is $285 \mathrm{C} $
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Work Step by Step

The total charge $ Q$ is given by $$ \begin{aligned} Q & =\iint_{D} \sigma(x, y) d A \\ &=\int_{0}^{5} \int_{2}^{5}(2 x+4 y) d y d x \\ & =\int_{0}^{5}\left[2 x y+2 y^{2}\right]_{y=2}^{y=5} d x \\ &=\int_{0}^{5}(10 x+50-4 x-8) d x=\int_{0}^{5}(6 x+42) d x \\ &=\left[3 x^{2}+42 x\right]_{0}^{5} \\ &=75+210 \\ &=285 \mathrm{C} \end{aligned} $$ Thus, the total charge is $ 285 \mathrm{C} $
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