Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places.
A) 0.556
B) 0.436
C) 0.673
D) 0.268
E) 0.883

Question

Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places. ​  ​  ​
A) 0.556 
B) 0.436 
C) 0.673 
D) 0.268 
E) 0.883

Quizplus · Accepted Answer

Using the Midpoint Rule with n = 4, we divide the interval [0,1] into 4 subintervals of equal width:
Δx = (1-0)/4 = 0.25
Then, we evaluate the function at the midpoint of each subinterval and multiply by the width of the subinterval:
f(0.125) = 0.67
f(0.375) = 0.78
f(0.625) = 0.74
f(0.875) = 0.46
Area ≈ Δx [f(0.125) + f(0.375) + f(0.625) + f(0.875)] = 0.25 [0.67 + 0.78 + 0.74 + 0.46] ≈ 0.673. 
Therefore, the best choice is (C).

Use the Midpoint Rule with N = 4 to Approximate