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
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Chapter1: Functions And Models
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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, 0)
(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.
Transcribed Image Text: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, 0) (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.
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