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2-136.
  1. Sketch a graph of the region bounded by the functions f(x) = x2, g(x) = −2x + 8, and the x-axis. Homework Help ✎

    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.