Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 16 - Multiple Integration - 16.6 Change of Variables - Exercises - Page 905: 18



Work Step by Step

We have $$ \operatorname{Jac}(G)=\frac{\partial(x, y)}{\partial(u, v)}=\left|\begin{array}{ll} {\frac{\partial x}{\partial u}} & {\frac{\partial x}{\partial v}} \\ {\frac{\partial y}{\partial u}} & {\frac{\partial y}{\partial v}} \end{array}\right|=\left|\begin{array}{ll} { e^v} & {ue^v} \\ {e^u} & {0} \end{array}\right| =-ue^{u+v}. $$
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