Consider an ellipse of the form x2 y + a = 1. b2 The circumference of...

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Consider an ellipse of the form x2 y + a = 1. b2 The circumference of this ellipse is given by the integral C = a sin (0) + b cos ()d0. So 0 This integral can be solved exactly if the ellipse is a circle. Then, a and b are equal to the radius of the circle r, and the circumference C = 2r, as you learned in your grade school days. If a and b are not equal to each other, then we can't solve the integral above exactly. a. Estimate C by the trapezoidal rule with N = 4 subintervals. Assume a and b are positive parameters. What you will find is an approximate formula for C as a function of a and b. b. Estimate C by Simpson's 1/3 rule with N = 4 subintervals. Assume a and b are positive parameters. What you will find is an approximate formula for C as a function of a and b. Consider an ellipse of the form x2 y + a = 1. b2 The circumference of this ellipse is given by the integral C = a sin (0) + b cos ()d0. So 0 This integral can be solved exactly if the ellipse is a circle. Then, a and b are equal to the radius of the circle r, and the circumference C = 2r, as you learned in your grade school days. If a and b are not equal to each other, then we can't solve the integral above exactly. a. Estimate C by the trapezoidal rule with N = 4 subintervals. Assume a and b are positive parameters. What you will find is an approximate formula for C as a function of a and b. b. Estimate C by Simpson's 1/3 rule with N = 4 subintervals. Assume a and b are positive parameters. What you will find is an approximate formula for C as a function of a and b.