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 15.5 - Triple Integrals in Rectangular Coordinates - Exercises 15.5 - Page 902: 42

Answer

3e -6

Work Step by Step

$\int^1_0 \int^1_0 \int^1_{x^2} 12xze^{zy^2}$ dy dx dz =$\int^1_0 \int^1_0 \int^\sqrt{y}_0 12xz e^{zy^2}$ dx dy dz =$\int^1_0 \int^1_0 6yz e^{zy^2}$ dy dz =$\int^1_0 [3e^{zy^2}]^1_0 dz $ =$3\int^1_0 (e^z-1)dz $ =$3[e^z-z]^1_0$ =$3e-6$
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