CPM Homework Help : APCALC Problem 2-9

For $f(x) = \sqrt {x-2}$ , he estimation of the area under the curve for $2 \le x \le 6$ is shown at right using four midpoint rectangles. Approximate the area using these rectangles. How reasonable is your result?

Hint:

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

More Help:

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

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

First quadrant grid on integer values from 0 to 7 on x axis, & from 0 to 4 on y axis, increasing curve opening down, starting at the point (2, comma 0), passing through (6, comma 2), & 4 shaded vertical bars, each with width of 1, starting at x = 2, bottom edges of bars on the x axis, midpoint of top edge of each bar, on the curve.