Answer
$15.2$
Work Step by Step
Step 1. Identify the x-coordinates of the rectangles (end points): range $[0,2]$, number of rectangles=$8$, x-coordinates $x_i=0.25,0.5,0.75,1,1.25,1.5,1.75,2$
Step 2. Use the given function $f(x)=9x-x^3$ to calculate the heights of the rectangles as shown in the table.
Step 3. Calculate the area by taking the sum of all the rectangle areas:
$$A=\sum^8_{i=1}0.25f(x_i)$$
Where $0.25$ is the width of the rectangles, and we can obtain $A\approx15.2$
