Elliptic integrals The length of the ellipsex=acost,y=bsint,0≤t≤2πx=acos⁡t,&nbsp;y=bsin⁡t,&nbsp;0≤t≤2πturns out to be=4a∫π/201−e2cos2t√dt=4a∫0π/21−e2cos2⁡tdtwhere ee&nbsp;is the ellipse's eccentricity. The integral in this formula, called an elliptic integral, is non elementary except when e=0e=0&nbsp;or 1 a. Use the Trapezoidal Rule with n=10n=10&nbsp;to estimate the length of the ellipse when a=1a=1&nbsp;and e=1/2e=1/2&nbsp;. b. Use the fact that the absolute value of the second derivative of f(t)=1−e2cos2t√f(t)=1−e2cos2⁡t&nbsp;is less than 1 to find an upper bound for the error in the estimate you obtained in part (a).

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Elliptic integrals The length of the ellipsex=acost,y=bsint,0≤t≤2πx=acos⁡t,&amp;nbsp;y=bsin⁡t,&amp;nbsp;0≤t≤2πturns out to be=4a∫π/201−e2cos2t√dt=4a∫0π/21−e2cos2⁡tdtwhere ee&amp;nbsp;is the ellipse&#039;s eccentricity. The integral in this formula, called an elliptic integral, is non elementary except when e=0e=0&amp;nbsp;or 1 a. Use the Trapezoidal Rule with n=10n=10&amp;nbsp;to estimate the length of the ellipse when a=1a=1&amp;nbsp;and e=1/2e=1/2&amp;nbsp;. b. Use the fact that the absolute value of the second derivative of f(t)=1−e2cos2t√f(t)=1−e2cos2⁡t&amp;nbsp;is less than 1 to find an upper bound for the error in the estimate you obtained in part (a).

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Elliptic integrals The length of the ellipsex=acost,y=bsint,0≤t≤2π

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