Chapter 8.8, Problem 73E

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

${\displaystyle {\int }_0^{2\pi }\sqrt{a^2{\cos }^{2}t+b^2{\sin }^{2}t}dt}$.

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