Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 15 - Multiple Integrals - Review - True-False Quiz - Page 1101: 3



Work Step by Step

Given that all the bounds are constant, we can rewrite the iterated integral: $\int_{1}^{2} \int_{3}^{4} x^2 e^y \, dy \, dx = \int_{1}^{2} x^2 \left( \int_{3}^{4} e^y \, dy \right) \, dx = \int_{3}^{4} e^y \, dy \int_{1}^{2} x^2 \, dx$. You can think about it as pulling out the constant $ \left( \int_{3}^{4} e^y \, dy \right) $ from the integral $ \int_{1}^{2} x^2 \left( \int_{3}^{4} e^y \, dy \right) \, dx$.
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