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graphThe function y = x3 + 1 is graphed at right, along with four left endpoint rectangles which approximate the area under the curve from x = –2 to x = 2. Homework Help ✎

  1. Why does it look like there are only three rectangles?

    What happens if the left endpoint is on the x-axis?

    Since f(−1) = 0, the height of the rectangle is 0.

  2. Recall that area under the x-axis is negative, while area above the x-axis is positive. Approximate the area under the curve for −2 ≤ x ≤ 2 using these four rectangles.

    Sum the areas of all four rectangles together. Remember to treat a rectangle's area as negative if it is below the x-axis.