The theorem goes on to state that the rectangles do not need to be of the same width. Thus our approximate area of 10.625 is likely a fairly good approximation. While some rectangles over-approximate the area, others under-approximate the area by about the same amount. In Figure 5.3.6 the function and the 16 rectangles are graphed. We were able to sum up the areas of 16 rectangles with very little computation. † † margin: 1 2 3 4 1 2 3 4 x y Figure 5.3.6: Approximating ∫ 0 4 ( 4 x - x 2 ) d x with the Right Hand Rule and 16 evenly spaced subintervals. SolutionUsing the formula derived before, using 16 equally spaced intervals and the Right Hand Rule, we can approximate the definite integral as
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