Use the Midpoint Rule n = 4 to approximate the area of the following region.
A) 2.748
B) 1.788
C) 1.875
D) 1.748
E) 3.951

Question

Use the Midpoint Rule n = 4 to approximate the area of the following region. ​  ​  ​
A) 2.748 
B) 1.788 
C) 1.875 
D) 1.748 
E) 3.951

Quizplus · Accepted Answer

Using the Midpoint Rule with n = 4, we divide the interval [0, 3] into 4 subintervals of equal width:

Δx = (3 - 0)/4 = 0.75

Then, we evaluate the function at the midpoint of each subinterval and multiply by the width:

f(0.375)Δx + f(1.125)Δx + f(1.875)Δx + f(2.625)Δx

= 1.125(0.75) + 1.548(0.75) + 1.548(0.75) + 1.125(0.75)

= 1.875

Therefore, the best choice is C, which is closest to our approximation of 1.875.

Use the Midpoint Rule N = 4 to Approximate the Area