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.
A) 10.892 sq units
B) 9.85 sq units
C) 9.545 sq units
D) 9.92 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. 
A) 10.892 sq units 
B) 9.85 sq units 
C) 9.545 sq units 
D) 9.92 sq units

Quizplus · Accepted Answer

To find the Riemann sum, we need to calculate the area of each rectangle and add them up. 
Width of rectangles = $\frac{1}{2}$ units
Height of each rectangle = midpoint of each subinterval on the graph of f.
So, the Riemann sum is given by: 
$R_n = \frac{1}{2}[f(0.25)+f(0.75)+f(1.25)+f(1.75)+f(2.25)+f(2.75)]$
Using the values from the graph, we get: 
$R_6 = \frac{1}{2}[2.00+1.75+1.25+1.00+1.50+1.25] = 9.875$
This is closest to option B) 9.85 sq units.

Find an Approximation of the Area of the Region R