Let the polar coordinate system be changed (for this problem only) by the introduction of a factor 2 into the r coordinate, r = 2r cos 0, y = r sin 0, so that the curves r = e are no longer circles, but ellipses, and call these coordinates (r, 0) elliptic polar coordinates. a (r, y) (a) Compute the Jacobian a (r, e) (b) Use part (a) to set up a double integral in elliptic polar coordinates that represents the area of the ellipse with major radius 2 and minor radius 1. Evaluate the integral.
Let the polar coordinate system be changed (for this problem only) by the introduction of a factor 2 into the r coordinate, r = 2r cos 0, y = r sin 0, so that the curves r = e are no longer circles, but ellipses, and call these coordinates (r, 0) elliptic polar coordinates. a (r, y) (a) Compute the Jacobian a (r, e) (b) Use part (a) to set up a double integral in elliptic polar coordinates that represents the area of the ellipse with major radius 2 and minor radius 1. Evaluate the integral.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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