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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (x – 4)° (y – 1)² 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) leading to a Jacobian of a(u, v) a(x, y) -dudv where the transformed region S is bounded by x² + y? = 1, we a(u, v) And since dA calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer.
Transcribed Image Text:In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (x – 4)° (y – 1)² 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) leading to a Jacobian of a(u, v) a(x, y) -dudv where the transformed region S is bounded by x² + y? = 1, we a(u, v) And since dA calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer.
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