Question: Consider the ellipse x2/a2 + y2/b2 = 1. a. Show that its perimeter is b The integral in part (a) is called an elliptic integral.

Consider the ellipse x2/a2 + y2/b2 = 1.
a. Show that its perimeter is

b The integral in part (a) is called an elliptic integral. It has been studied at great length, and it is known that the inte-grand does not have an elementary antiderivative, so we must turn to approximate methods to evaluate P. Do so when a = 1 and e = 1/4 using the Parabolic Rule with n = 4. (Your answer should be near 2Ï€. Why?)
(c) Repeat part (b) using n = 20.

1 e cos t dt,

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