Notice that the graph of f(x) is a downward-opening parabola with vertex at (0, 9) and x-intercepts at (-3, 0) and (3, 0). So the graph of f(x) ---Select--- ✓ lie on or above the x-axis over the interval [1, 3]. To approximate the area under the curve, we use the areas of rectangles whose bases are on the x-axis and whose heights are the vertical distances from points on their bases to the curve. We divide the interval [1, 3] into n = 4 equal subintervals and use them as the bases of n rectangles whose heights are determined by the curve. (See the figure below.) 10 y −1 8 4 2 1 2 Notice that the figure shows that using left-endpoints will give an approximation that ---Select--- The width of each of these rectangles is the result of dividing the length of the interval [1, 3] by n = 4. Determine the width of each rectangle. the length of the interval width = = = 31 4 n the true area.

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