Show that the total length of the ellipse x = a sin(8), y = b cos(8), a > b > 0, is TT/2 ™¹²2 √ ₁ – e² sin²(0) dº L = 4a where e is the eccentricity of the ellipse described by e = y (e=, where c here c = √3² - 6²). a

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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Show that the total length of the ellipse x = a sin(8), y = b cos(8), a > b > 0, is
TT/2
√¹/² √1 - e² sin² (0) de
L = 4a
where e is the eccentricity of the ellipse described by (e ==
a
where c =
le
√3²-6²).
2
Transcribed Image Text:Show that the total length of the ellipse x = a sin(8), y = b cos(8), a > b > 0, is TT/2 √¹/² √1 - e² sin² (0) de L = 4a where e is the eccentricity of the ellipse described by (e == a where c = le √3²-6²). 2
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