Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 15 - Multiple Integrals - 15.10 Exercises - Page 1071: 10

Answer

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

Work Step by Step

Let us consider $u^2+v^2 \leq 1$ Also, we have $x=au\\ u=\dfrac{x}{a}$ (simplify) and $y=bv \\ v=\dfrac{y}{b}$(simplify) Therefore, the values of $u$ and $v$ are: $u=\dfrac{x}{a}$ and $ v=\dfrac{y}{b}$ Thus, the equation of the ellipse is: $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$ Hence, the region is inside the ellipse $(\dfrac{x}{a})^2+(\dfrac{y}{b})^2 \leq 1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.