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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.

Definitions:

Variable Overhead Efficiency Variance

A measure used in management accounting to assess the efficiency of variable production overhead based on the actual time taken to produce goods versus the expected time.

Standard Direct Labor-Hours

Standard direct labor-hours refer to the estimated hours of direct labor work required to produce one unit of a product or service, used for budgeting and variance analysis.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the standard cost assigned to those overheads, indicating efficiency in managing variable costs.

Direct Materials Purchases Variance

the difference between the actual cost of direct materials purchased and the expected (or standard) cost, indicating how effectively a company is managing its resources.