### Home > CALC > Chapter 2 > Lesson 2.4.1 > Problem2-136

2-136.

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

1. How could you estimate the area in this region?

2. Using your method, estimate the area of the region.

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?

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 $2 ≤ x ≤ 4$.

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