Question

Consider the region under the curve of the following function. Estimate the area of the region using the left endpoints and right endpoints, respectively. If necessary, round your answers to five decimal places. f(x)=x²+5 for a=-7, b+-2 and n=16

a. Left Endpoints: [insert numerical value]
Right Endpoints: [insert numerical value]
b. Left Endpoints: [insert numerical value]
Right Endpoints: [insert numerical value]
c. Left Endpoints: [insert numerical value]
Right Endpoints: [insert numerical value]
d. Left Endpoints: [insert numerical value]
Right Endpoints: [insert numerical value]

Answer 1

Using the Riemann sum method with left and right endpoints and 16 subdivisions, we can estimate the area under the function f(x) = x² + 5 between a = -7 and b = -2 by summing up the areas of rectangles formed at those endpoints, multiplied by the interval width.

Step-by-step explanation:

To estimate the area under the curve of the function f(x) = x² + 5 from a = -7 to b = -2 with n = 16 subdivisions, we use the Riemann sum method with left and right endpoints. The interval length is (b - a)/n, which equals (-2 - (-7))/16 = 5/16. We then evaluate the function at each left endpoint starting at a and moving right, and at each right endpoint starting at a + (5/16) and moving right. Each evaluation is then multiplied by the interval length to calculate the area of each rectangle, and the sum of these areas will approximate the total area under the curve.