Find an approximation of the area of the region R under the graph of f by computing the Riemann sum of f corresponding to the partition of the interval into the subintervals shown in the accompanying figures.Use the midpoints of the subintervals as the representative points.Round your answer to the nearest hundredth.
A)1.92 sq units
B)0.85 sq units
C)2.27 sq units
D)2.34 sq units

Question

Find an approximation of the area of the region R under the graph of f by computing the Riemann sum of f corresponding to the partition of the interval into the subintervals shown in the accompanying figures.Use the midpoints of the subintervals as the representative points.Round your answer to the nearest hundredth. 
A)1.92 sq units 
B)0.85 sq units 
C)2.27 sq units 
D)2.34 sq units

Quizplus · Accepted Answer

The Riemann sum can be computed as: 
$$\Delta x\left(f\left(\frac{1}{8}ight)+f\left(\frac{3}{8}ight)+f\left(\frac{5}{8}ight)+f\left(\frac{7}{8}ight)ight)$$
where $\Delta x = \frac{1}{4}$ is the width of each subinterval and the representative points are the midpoints of each subinterval. Using the graph, we can see that $f\left(\frac{1}{8}ight) \approx 0.5$, $f\left(\frac{3}{8}ight) \approx 1$, $f\left(\frac{5}{8}ight) \approx 2$, and $f\left(\frac{7}{8}ight) \approx 1.5$. Plugging in these values, we get:
$$\frac{1}{4}(0.5+1+2+1.5) = \frac{5}{4} \approx 2.27$$
Rounding to the nearest hundredth gives us $\boxed{	extbf{(C) }2.27 	ext{ sq units}}$.

Find an Approximation of the Area of the Region R