a) Estimate the area under the graph of f(x) = 3/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. (Round your answer to four decimal places.)

Question

b) Repeat part (a) using left endpoints. (Round your answer to four decimal places.)

Answer 1

a)

The area under the curve approximated by the rectangles formed by the RIGHT endpoints of each section is:

Area 1: (2.4)(0.25)

Area 2: (2)(0.25)

Area 3: (12/7)(0.25)

Area 4: (1.5)(0.25)

Total area = (2.4)(0.25) + (2)(0.25) + (12/7)(0.25) + (1.5)(0.25)

Total area = (0.25)(2.4 + 2 + 12/7 + 1.5)

Total area = (0.25)(533/70)

Total area = 533/280 = 1.9036

b) Using the left endpoints we get:

Area 1: (3)(0.25)

Area 2: (2.4)(0.25)

Area 3: (2)(0.25)

Area 4: (12/7)(0.25)

Total area = (3)(0.25) + (2.4)(0.25) + (2)(0.25) + (12/7)(0.25)

Total area = (0.25)(3 + 2.4 + 2 + 12/7)

Total area = (0.25)(319/35)

Total area = 319/140 = 2.2786

Note that the true area under the curve can be better approximated by averaging these.