Calculus: Early Transcendentals 8th Edition

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

Chapter 15 - Section 15.9 - Change of Variables in Multiple Integrals - 15.9 Exercise - Page 1060: 4



Work Step by Step

Here, we have $\dfrac{\partial x}{\partial p}=e^q$ and $\dfrac{\partial x}{\partial q}=p e^q$ Also, $\dfrac{\partial y}{\partial p}=q e^p$ and $\dfrac{\partial y}{\partial q}= e^p$ Now, $Jacobian =\begin{vmatrix} \dfrac{\partial x}{\partial p}&\dfrac{\partial x}{\partial q}\\\dfrac{\partial y}{\partial p}&\dfrac{\partial y}{\partial q}\end{vmatrix}=\begin{vmatrix} e^q&pe^q\\ qe^p&e^p\end{vmatrix}=e^{p+q}-pqe^{p+q}=(1-pq)e^{p+q}$
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