In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (y – 1)? (x – 4)? of the area of a circle. For example, consider R, the region bounded by the ellipse 4 36 = 1. The easiest transformation to choose makes and v = which should be easily inverted to obtain and y = a(x, y) a(u, v) leading to a Jacobian of %3D a(x, y) - dudv where the transformed region S is bounded by a? + y² = 1, we And since calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer.

In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (y – 1)? (x – 4)? of the area of a circle. For example, consider R, the region bounded by the ellipse 4 36 = 1. The easiest transformation to choose makes and v = which should be easily inverted to obtain and y = a(x, y) a(u, v) leading to a Jacobian of %3D a(x, y) - dudv where the transformed region S is bounded by a? + y² = 1, we And since calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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