How can I find the minimum number of open rectangles in a grid?

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph?

• Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given ...show more

• Answer:

  1/4*{[(2(3)^2-3-1) + (2(3.5)^2-3.5-1)] + [(2(3.5)^2-3.5-1) + (2(4)^2-4-1)] + [(2(4)^2-4-1 + (2(4.5)^2-4.5-1)] + [(2(4.5)^2-4.5-1) + (2(5)^2-5-1)]} = 1/4[34 + 47 + 62 + 79] = 55.5 Actual area = Int 3to5 [2x^2-x-1 dx] = [2/3(5)^3 - 1/2(5)^2 - 5] - [2/3(3)^3 - 1/2(3)^2 - 3] 65.8333 - 10.5 = 55.3333