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: 10


The region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$

Work Step by Step

Given: $u^2+v^2 \leq 1$ Then , we have $x=au$ or, $u=\dfrac{x}{a}$ and $y=bv$ or, $v=\dfrac{y}{b}$ Therefore,we get $u=\dfrac{x}{a}$ and $ v=\dfrac{y}{b}$ Now, $u^2+v^2 \leq 1 \implies (\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$ Hence, the region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
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