CPM Homework Help : CALC Problem 2-136

Sketch a graph of the region bounded by the functions $f(x) = x^2$ , $g(x) = −2x + 8$ , and the $x$ -axis.

How could you estimate the area in this region?
Using your method, estimate the area of the region.

Hint (a):

Graph the functions. Shade the region. Find all relevant intersections: Where does $f(x)$ intersect with $g(x)$ ? Where does each function cross the $x$ -axis? How many integrals will you need?

More Help (a):

The functions intersect at ( $2, 4$ ). The area should be approximated with rectangles or trapezoids for $0 ≤ x ≤ 2$ and added to the area of the triangle for $2 ≤ x ≤ 4$ .

Answer (b):

Estimates will vary. area $\approx \frac{1}{500}\sum_{n=0}^{999}\Big(\frac{n}{500}\Big)^2+\frac{1}{2}(2)(4)\approx 6.66\text{ units}^2$