The length of an ellipse with axes of length 2a and 2b is given below, where e is the ellipse's eccentricity. The integral in this formula, called an elliptic integral, is nonelementary except when e = 1 or 0. Complete parts (a) and (b) below. Length = 4a Л 2 √ √₁-e² cos ²t dt, e = - 0 a²-b² a 1 a. Use the Trapezoidal Rule with n = 10 to estimate the length of the ellipse when a = 4 and e= (Round to three decimal places as needed.) b. Use the fact that the absolute value of the second derivative of f(t)=√√1-e² cos ²t is less than 1 to find an upper bound for the error in the estimate you obtained in part (a). E-≤ (Round to four decimal places as needed.)
The length of an ellipse with axes of length 2a and 2b is given below, where e is the ellipse's eccentricity. The integral in this formula, called an elliptic integral, is nonelementary except when e = 1 or 0. Complete parts (a) and (b) below. Length = 4a Л 2 √ √₁-e² cos ²t dt, e = - 0 a²-b² a 1 a. Use the Trapezoidal Rule with n = 10 to estimate the length of the ellipse when a = 4 and e= (Round to three decimal places as needed.) b. Use the fact that the absolute value of the second derivative of f(t)=√√1-e² cos ²t is less than 1 to find an upper bound for the error in the estimate you obtained in part (a). E-≤ (Round to four decimal places as needed.)
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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Transcribed Image Text:The length of an ellipse with axes of length 2a and 2b is given below, where e is the ellipse's eccentricity. The
integral in this formula, called an elliptic integral, is nonelementary except when e = 1 or 0. Complete parts (a)
and (b) below.
플
Length = 4a √1-²
0
√₁²-6²
²tdt, e=
COS
a
11/1/1
a. Use the Trapezoidal Rule with n=10 to estimate the length of the ellipse when a = 4 and e=
(Round to three decimal places as needed.)
b. Use the fact that the absolute value of the second derivative of f(t)=√1-e² cos ²t is less than 1 to find an
upper bound for the error in the estimate you obtained in part (a).
E-≤ (Round to four decimal places as needed.)
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