10:20 AM Wed Apr 19 Tutorial Exercise Find the sum of the areas of the shaded rectangles under the graph. [Hint: The width of each rectangle is the difference between the x-values at its base. The height of each rectangle is the height of the curve at the left edge of the rectangle] 1 1.25 1.5 1.75 2 (D Step1 4 The sum of the areas of the rectangles approximates the area under the curve, though not very well. Notice that every rectangle extends aaove the curve f(x) = , and hence the X rectangles provide an overestimate of the area. To nd the areas of the rectangles, we recall (or look up in the text) the formula for the area of a rectangle: A = hw \J/ luv where h is the height and w is the width. We will need the width and height of each rectangle. Step 2 Now, we note that the bases of the rectangles in the image are all the same size. Taking the difference between the left and right endpoints of the first rectangle, we have the following. width = Ax = 0.25 J 7/ 0.25 We have the widths; now we need the heights in order to find the areas. (Round your answers to four decimal places when necessary.) The height of the first rectangle is f(1) = g = In like fashion, we find the following. r._ L. 10:20 AM Wed Apr 19 . . . @ 100% webassign.net 2 1 1.25 1.5 1.75 2 Step 1 The sum of the areas of the rectangles approximates the area under the curve, though not very well. Notice that every rectangle extends above the curve f(x) = -, and hence the rectangles provide an overestimate of the area. To find the areas of the rectangles, we recall (or look up in the text) the formula for the area of a rectangle: A = hw where h is the height and w is the width. We will need the width and height of each rectangle. Step 2 Now, we note that the bases of the rectangles in the image are all the same size. Taking the difference between the left and right endpoints of the first rectangle, we have the following. width = Ax = 0.25 0.25 Step 3 We have the widths; now we need the heights in order to find the areas. (Round your answers to four decimal places when necessary.) The height of the first rectangle is f( 1) = = = 4 In like fashion, we find the following. f(1.25) = 1.6 X f(1.5) = 1.3333 X f(1.75) = 1.1429 X Submit Skip (you cannot come back) Need Help? Read It