The rectangles in the figure below illustrate a right endpoint Riemann sum for f(x) = = The value of this right endpoint Riemann sum is vertical lines x = 4 and x = 8. 8 7 6 5 3 2 1 y 1 x 10 on the interval [4, 8]. and this Riemann sum is [select an answer] the area of the region enclosed by y = f(x), the x-axis, and the 2 3 4 5 6 7 Right endpoint Riemann sum for y=ton [4, 8] 8 X A f(x) for 0 x 3.5 is shown above. In the figure, A, B, and C represent the (positive) areas of the regions between the function and the x-axis on the intervals [0, 1], [1,2], and [2,3], The curve y= respectively. 8 b) Recalling that Rg = f(x)A, fill in the details for the term with index i = 5: i=1 c) Given that A = 1.8, B = 1.6 and C = 3.6, a) Let Rg denote the Riemann sum with right endpoints approximating area C with 8 rectangles. Select the most informative description of the relationship between Rg and C: Rg is greater than C Rg is less than C Rg is equal to C O No relationship can be determined. [ f(x) dx = B calculate the definite integral C Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 5 using a right Riemann sum with four approximating rectangles. R = Sketch the graph and the rectangles defining R4, then complete this statement: the exact area, A. R4 is ? The width wn in meters, at various points on along the fairway of a golf course changes as shown in the figure below. The values of wn and an in meters are given in the table below the figure. -FFFFFFFED- (Click on the figure for a larger version--note that you may have to resize the window you get to get a nice picture.) The values of In and Wn are n = 0 1 2 3 4 5 6 7 8 9 10 n = 0120 240 360 480 600 720 840 960 1080 1200 Wn 0 75 77 79 84 76 68 73 75 75 0 amount of fertilizer = If one kilogram of fertilizer covers 250 square meters, find a reasonable estimate for the amount of fertilizer needed to fertilize the fairway. kilograms = 5. a) Approximate I using Simpson's Rule with n = 4 subintervals. Consider the integral I = 3 (x - 4x + 2x+1) dx. S4= b) Find the exact value of the integral. I = So Use both the Trapezoidal Rule and Simpson's rule to estimate the integral In both cases, use all the information in the following table of values for f. x 13 14 15 16 17 18 19 f(x) 2.6 2.2 3.1 3.2 3.2 2.4 1.4 Trapezoid Rule approximation T = Simpson's Rule approximation Sn 19 f(x) dx. Below is the graph of the function y = f(x). 1,0 Answer: S6 1.0 Use Simpson's Rule with 6 subintervals to estimate the area under the curve from x = 0 to x = 6.