The function y = x3 + 1 is graphed below, along with four left endpoint rectangles which approximate the area from x = −2 to x = 2. Homework Help ✎
Why does it look like there are only three rectangles?
Recall that area under the x-axis is negative, while that above the x-axis is positive. Approximate A(y, −2 ≤ x ≤ 2) using these four rectangles.
What happens if the left endpoint is on the x-axis?
Since f(−1) = 0, the height of the rectangle is 0.
Sum the areas of all four rectangles together. Remember to treat a rectangle's area as negative if it is below the x-axis.