Final Exam Study Guide Problem 7 Solution

Problem 7 deal with approximating area under a function using rectangles. This information is covered in Section 13.2.

Problem 7 Let final_exam_sg_7a. In this problem, we are interested in estimating the area under the graph and above the x axis from x = 1 to x = 5.

a. Approximate the area described above by drawing 4 rectangles on the graph below where the rectangle’s heights are determined by the left hand side of the rectangle (left hand sum).

Solution

final_exam_sg_7bb. Write out 4 terms in a sum corresponding to the areas of the rectangles drawn in part a.

Solution

final_exam_sg_7c

c. Approximate the area described above by drawing 4 rectangles on the graph below where the rectangle’s heights are determined by the right hand side of the rectangle (right hand sum).

Solution

final_exam_sg_7d

d. Write out 4 terms in a sum corresponding to the areas of the rectangles drawn in part c.

Solution

final_exam_sg_7e