Answer
$7.25$
Work Step by Step
Step 1. Based on the figure given by the Exercise, there are 4 rectangles using right endpoint approximations.
The x-coordinates of these endpoints are $x_i=1.5,2,2.5,3$
Step 2. Given the equation $f(x)=4x-x^2$, the corresponding heights of the rectangles can be calculated as shown in the table.
Step 3. To estimate the area, we add up the areas $A_i$ of the rectangles (width=0.5) as:
$A=\sum A_i=0.5(3.75+4+3.75+3)=7.25$
