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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 - 5)² (y-2)² 49 36 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes U= which should be easily inverted to obtain leading to a Jacobian of a(x, y) (u, v) and v And since •[₁₁A= [[₁² dA 8(x, y) (u, v) calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer. and y + dudu where the transformed region S is bounded by x2 + y² = 1, we

In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (x - 5)² (y-2)² 49 36 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes U= which should be easily inverted to obtain leading to a Jacobian of a(x, y) (u, v) and v And since •[₁₁A= [[₁² dA 8(x, y) (u, v) calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer. and y + dudu where the transformed region S is bounded by x2 + y² = 1, we

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 (y-2)² (x - 5)² 36 49 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes U= which should be easily inverted to obtain x = leading to a Jacobian of and v= a(x, y) d(u, v) And since and y = a (x, y) • [[₁₂₁A = 1₂₁²₁ || a(t,r) dA calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer. -dudu where the transformed region S is bounded by x² + y² = 1, we
Transcribed Image Text:In order to find the area of an ellipse, we may make use of the idea of transformations and our knowledge (y-2)² (x - 5)² 36 49 of the area of a circle. For example, consider R, the region bounded by the ellipse = 1. The easiest transformation to choose makes U= which should be easily inverted to obtain x = leading to a Jacobian of and v= a(x, y) d(u, v) And since and y = a (x, y) • [[₁₂₁A = 1₂₁²₁ || a(t,r) dA calculate the area by multiplying the area and the Jacobian, arriving at Give an exact answer. -dudu where the transformed region S is bounded by x² + y² = 1, we
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