33. a. Parametrization of an ellipsoid The parametrization x = a cos 0, y = b sin 0, 0 < 0 < 27 gives the ellipse (x²/a²) + (y²/b²) = 1. Using the angles 0 and ø in spheri- cal coordinates, show that r(0, 4) = (a cos 0 sin ø)i + (b sin 0 sin ø)j + (c cos 4)k is a parametrization of the ellipsoid (x²/a²) + (y²/b²) + (z²/c²) = 1. b. Write an integral for the surface area of the ellipsoid, but do not evaluate the integral.
33. a. Parametrization of an ellipsoid The parametrization x = a cos 0, y = b sin 0, 0 < 0 < 27 gives the ellipse (x²/a²) + (y²/b²) = 1. Using the angles 0 and ø in spheri- cal coordinates, show that r(0, 4) = (a cos 0 sin ø)i + (b sin 0 sin ø)j + (c cos 4)k is a parametrization of the ellipsoid (x²/a²) + (y²/b²) + (z²/c²) = 1. b. Write an integral for the surface area of the ellipsoid, but do not evaluate the integral.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:33. a. Parametrization of an ellipsoid The parametrization
x = a cos 0, y = b sin 0, 0 < 0 < 27 gives the ellipse
(x²/a²) + (y²/b²) = 1. Using the angles 0 and ø in spheri-
cal coordinates, show that
r(0, 4) = (a cos 0 sin ø)i + (b sin 0 sin ø)j + (c cos 4)k
is a parametrization of the ellipsoid (x²/a²) + (y²/b²) +
(z²/c²) = 1.
b. Write an integral for the surface area of the ellipsoid, but do
not evaluate the integral.
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