Elliptic integrals The length of the ellipse
turns out to be
where e is the ellipse's eccentricity. The integral in this formula, called an elliptic integral, is non elementary except when e=0 or 1 a. Use the Trapezoidal Rule with n=10 to estimate the length of the ellipse when a=1 and e=1/2 . b. Use the fact that the absolute value of the second derivative of f(t)=1−e2cos2t√ is less than 1 to find an upper bound for the error in the estimate you obtained in part (a).