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. √₁²-b² train Length = 4a √1-e² cos ²1 dt, e= a 0 1 2 a. Use the Trapezoidal Rule with n = 10 to estimate the length of the ellipse when a = 3 and e CALL (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). Els (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. √₁²-b² train Length = 4a √1-e² cos ²1 dt, e= a 0 1 2 a. Use the Trapezoidal Rule with n = 10 to estimate the length of the ellipse when a = 3 and e CALL (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). Els (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.
ਪਦਾਰ
Length = 4a √1-
0
a²-b²
²tdt, e=-
-e² COS
a
1
a. Use the Trapezoidal Rule with n = 10 to estimate the length of the ellipse when a = 3 and e=
2
|ET|≤
(Round to three decimal places as needed.)
b. Use the fact that the absolute value of the second derivative of f(t) =
(Round to four decimal places as needed.)
1-e² cos ²t is less than 1 to find an upper bound for the error in the estimate you obtained in part (a).
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