Answer
$3.83$
Work Step by Step
Step 1. Based on the figure given by the Exercise, there are six rectangles using right endpoint approximations.
The x-coordinates of these endpoints are $x_i=0.5,1,1.5,2,2.5,3$
Step 2. Given the equation $f(x)=\sqrt x$, 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 six rectangles (width=0.5) as:
$A=\sum A_i=0.5(0.71+1+1.22+1.41+1.58+1.73)=3.83$
