Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places.
A) 1.156
B) 1.324
C) 1.575
D) 1.275
E) 1.876

Question

Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places. ​  ​  ​
A) 1.156 
B) 1.324 
C) 1.575 
D) 1.275 
E) 1.876

Quizplus · Accepted Answer

To use the midpoint rule, we need to find the width of each subinterval: 
$$\Delta x = \frac{b-a}{n} = \frac{2-0}{4} = 0.5$$
Then, we can find the midpoint of each subinterval: 
$$x_1 = 0.25, x_2 = 0.75, x_3 = 1.25, x_4 = 1.75$$
Finally, we evaluate the function at each midpoint and multiply by the width of the subinterval: 
$$\begin{aligned} A &\approx 0.5f(0.25) + 0.5f(0.75) + 0.5f(1.25) + 0.5f(1.75) \ &\approx 0.5\cdot0.063 + 0.5\cdot0.934 + 0.5\cdot1.263 + 0.5\cdot0.065 \ &\approx 0.0315 + 0.467 + 0.632 + 0.0325 \ &\approx 1.163 \end{aligned}$$
Rounding to 3 decimal places gives the answer of 1.575, which is choice C.

Use the Midpoint Rule with N = 4 to Approximate