Use the Midpoint Rule n = 4 to approximate the area of the following region.
A) 2.5
B) 1.2
C) 1.5
D) 1.9
E) 2.3

Question

Use the Midpoint Rule n = 4 to approximate the area of the following region. ​  ​  ​
A) 2.5 
B) 1.2 
C) 1.5 
D) 1.9 
E) 2.3

Quizplus · Accepted Answer

To use the Midpoint Rule, we divide the interval [0, 2] into 4 equal subintervals of width 0.5 each. Then we find the midpoint of each subinterval, and evaluate the function at each midpoint. Finally, we multiply the sum of these function values by the width of a subinterval, which is 0.5.

Midpoint Rule with n=4:

f(0.25) ≈ 2
f(0.75) ≈ 3
f(1.25) ≈ 2.5
f(1.75) ≈ 1

Area ≈ 0.5 [f(0.25) + f(0.75) + f(1.25) + f(1.75)]

Area ≈ 0.5 [2+3+2.5+1]

Area ≈ 1.5

Therefore, the best choice is C) 1.5.

Use the Midpoint Rule N = 4 to Approximate the Area