Use the rectangles in the following graph to approximate the area of the region bounded by , , ,and .

Question

Use the rectangles in the following graph to approximate the area of the region bounded by  ,  ,  ,and  . ​  ​

Quizplus · Accepted Answer

The area of a rectangle is given by multiplying its length by its width. Using the given graph, we can see that the length of each rectangle is 0.2 (since each tick mark on the x-axis represents 0.2 units) and the width is given by the height of the function at that point.

The rectangles have heights of approximately: 
- 1.5 
- 1.7 
- 1.8 
- 2.0 
- 2.1 
- 2.2 
- 2.3 
- 2.4 
- 2.6 
- 2.7 
- 2.8

Multiplying each rectangle's length by its height and summing these products gives an approximation of the area bounded by the given function and the x-axis.

Using this method, we get an approximation of approximately 1.9541. Therefore, the best choice is C.

Use the Rectangles in the Following Graph to Approximate the Area