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Consider the Ellipse Pictured Below: the Perimeter of the Ellipse

question 19

Short Answer

Consider the ellipse pictured below: $Consider the ellipse pictured below: The perimeter of the ellipse is given by the integral \int_{0}^{\pi / 2} 8 \sqrt{1-\frac{3}{4} \sin ^{2} \theta} d \theta .It turns out that there is no elementary antiderivative for the function f(\theta)=8 \sqrt{1-\frac{3}{4} \sin ^{2} \theta} , and so the integral must be evaluated numerically.A graph of the integrand f( \theta )is shown below. Calculate the right sum that approximates the definite integral with N = 4 equal divisions of the interval.Round to 4 decimal places.$ The perimeter of the ellipse is given by the integral $\int_{0}^{\pi / 2} 8 \sqrt{1-\frac{3}{4} \sin ^{2} \theta} d \theta$ .It turns out that there is no elementary antiderivative for the function $f(\theta)=8 \sqrt{1-\frac{3}{4} \sin ^{2} \theta}$ , and so the integral must be evaluated numerically.A graph of the integrand f( $\theta$ )is shown below. $Consider the ellipse pictured below: The perimeter of the ellipse is given by the integral \int_{0}^{\pi / 2} 8 \sqrt{1-\frac{3}{4} \sin ^{2} \theta} d \theta .It turns out that there is no elementary antiderivative for the function f(\theta)=8 \sqrt{1-\frac{3}{4} \sin ^{2} \theta} , and so the integral must be evaluated numerically.A graph of the integrand f( \theta )is shown below. Calculate the right sum that approximates the definite integral with N = 4 equal divisions of the interval.Round to 4 decimal places.$ Calculate the right sum that approximates the definite integral with N = 4 equal divisions of the interval.Round to 4 decimal places.

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