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For , he estimation of the area under the curve for is shown at right using four midpoint rectangles. Approximate the area using these rectangles. How reasonable is your result? 

for all rectangles. Height is determined by the function, evaluated at midpoints.

First quadrant  grid on integer values from 0 to 7 on x axis, & from 0 to 4 on y axis, increasing curve opening down, starting at the point (2, comma 0), passing through (6, comma 2), & 4 shaded vertical bars, each with width of 1, starting at x = 2, bottom edges of bars on the x axis, midpoint of top edge of each bar, on the curve.