Question

+1 4 In each of the following graphs there are six rectangles. The area under the graph of f(x) between the vertical lines x=0, x=2 and the x-axis is also shaded RRRR 051 152 RRRRRR • Approximate the area under the curve by considering a lower bound and an upper bound. Why do you think that more rectangles are being used? • Complete the following tables to organize the information. You can create a table with your GDC to calculate the heights of the rectangles. How would you calculate the widths? Remember that they are all equal • Lower bound with six rectangles: Rectangle Width Height Area • Upper bound with six rectangles: Rectangle Height • What do you notice? Are the lower and upper bounds closer to each other than when you had four rectangles? How do you think these estimates can be improved? • Write a new inequality relating L U and A

Answer 1

DATE: TTT @ lower bound; Rectangle Area Height 1 119 11/27 13/9 13/21 3 25/27 LA 34/27 Ls = 4.074 Upper bound :- Rectangle Heid Area. 11/27 13/9 13/27 2579 34/9 45/21 34/27 I = 5.407 - a Increasing no. of Rectangles con émprove the result. Ls <A< Us I Aug. of Ls & Us can give nearly accurate value A.