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.)

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...

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