Estimate the area under the graph of f(x) = 3/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. (Round your answer to four decimal places.)
Accepted Solution
A:
Answer: area ≈ 1.9036Step-by-step explanation:Dividing the interval from x=1 to x=2 into 4 rectangles of equal width means that each has a width of (2-1)/4 = 1/4. Then for n=1 to 4, the x-coordinate of the point at the right end of the rectangle is ... xn = 1 + (n/4)and the corresponding y-values will be yn = f(xn) = 3/xnThe area is the product of yn and the width of the rectangle, so will be the sum ... area = (1/4)y1 + (1/4)y2 + (1/4)y3 + (1/4)y4It is convenient to use a graphing calculator or spreadsheet to find and sum these values. The attached shows the sum to be ... (1/4)(2.4 + 2 + 1.71429 + 1.5) = 7.61429/4 ≈ 1.9036