Question

Given the equation, y=x 2−27, a range of x from -2 to 7 , and an estimation using 4 rectangles; how does the right Riemann sum compare to the actual area? a. Riemann sum is more than 5 more than the actual area. b. Riemann sum is more than 5 less than the actual area. c. Riemann sum is within 5 of the actual area. d. Riemann sum is exactly the actual area.

Answer 1

To compare the right Riemann sum to the actual area, we can find the exact area under the curve using integration.

Step-by-step explanation:

The right Riemann sum is an approximation of the area under a curve using rectangles. In this case, the curve is given by the equation y = x^2 - 27 and the range of x is from -2 to 7. To estimate the area using 4 rectangles, we divide the range into 4 equal intervals: [-2, -1], [-1, 1], [1, 4], and [4, 7]. We then find the height of each rectangle by evaluating the function at the right endpoint of each interval, and compute the area by multiplying the height by the width of each rectangle.

To compare the right Riemann sum to the actual area, we can find the exact area under the curve using integration. By integrating the function y = x^2 - 27 over the range [-2, 7], we can find the actual area. Comparing the right Riemann sum to the actual area, we can determine if the sum is more or less than the actual area.