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 area of Region R can be approximated by computing the Riemann sum. Using the midpoint method, the representative points will be at (0.25, 1), (0.75, 3), (1.25, 2), (1.75, 2), and (2.25, 1), and the subinterval width is 0.5. Thus, the Riemann sum is:

0.5(1+3+2+2+1) = 2.5

Rounding to the nearest hundredth gives an approximation of 2.27 square units, which corresponds to choice C.

Find an Approximation of the Area of the Region R