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

2-136.

Sketch a graph of the region bounded by the functions

*f*(*x*) =*x*^{2},*g*(*x*) = −2*x*+ 8, and the*x*-axis. Homework Help ✎How could you estimate the area in this region?

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.