Calculus 8th Edition

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

Chapter 15 - Multiple Integrals - 15.9 Change of Variables in Multiple Integrals - 15.9 Exercises - Page 1100: 1



Work Step by Step

Since, $Jacobian =\begin{vmatrix} \dfrac{\partial x}{\partial a}&\dfrac{\partial x}{\partial b}\\\dfrac{\partial y}{\partial a}&\dfrac{\partial y}{\partial b}\end{vmatrix}$ Here, we have $\dfrac{\partial x}{\partial a}=2$ and $\dfrac{\partial x}{\partial b}=1$ Also, $\dfrac{\partial y}{\partial a}=4$ and $\dfrac{\partial y}{\partial b}=-1$ Now, $Jacobian =\begin{vmatrix} 2&1\\4&-1\end{vmatrix}=2 \times (-1) -4 \times 1=-2-4=-6$
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