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Consider an ellipse with major (x ) radius a and minor (y ) radius b ....

Consider an ellipse with major (x ) radius a and minor (y ) radius b .

(a) Compute the area exactly.

(b) Compute the area using Simpsons rule with n = 8 partitions in x .

(c) What is the error using Simpsons rule? Does this make sense?

(d) Find an integral expression for the arc length of the ellipse, and evaluate the integral when b = a.

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