### Home > CALC > Chapter 2 > Lesson 2.1.1 > Problem2-9

2-9.

For $f ( x ) = \sqrt { x - 2 }$, the estimation of $A(f, 2 ≤ x ≤ 6)$ is shown below using four midpoint rectangles. Calculate $A(f, 2 ≤ x ≤ 6)$ using these rectangles. How reasonable is your result?

$A =$ (base)(height)
Base $= 1$ for all rectangles. Height is determined by the function, evaluated at midpoints.

The height of the smallest rectangle is $\sqrt{0.5}.$
The height of the largest rectangle is $\sqrt{3.5}.$