Barrons AP Calculus

(c)

approximating   sum is

.

This    sum uses    the circumscribed   rectangles  shown   in  Figure  N6–4.

Figure  N6–4

Figure  N6–5

The midpoint    sum uses    the heights at  the midpoints   of  the subintervals,   as

shown   in  Figure  N6–5.   The approximating   sum is