Arc length of an ellipse The length of an ellipse with axes of length 2a and 2b is

\(\int_{0}^{2 \pi} \sqrt{a^{2} \cos ^{2} t+b^{2} \sin ^{2} t} d t\) .

Use numerical integration and experiment with different values of n to approximate the length of an ellipse with a=4 and b=8.

Problem 49EArc length of an ellipse The length of an ellipse with axes of length 2a and 2b is Use numerical integration and experiment with different values of n to approximate the length of an ellipse with a =4 and b = 8.SolutionStep 1In this problem we have to find the arc length of the ellipse, we have to use numerical integration and experiment with different values of n to approximate the length of an ellipse with a =4 and b = 8Consider We perform Simpson’s method for approximation, using , n = 6 and n = 8.