Barrons AP Calculus

(d)

.

Since the exact value of or 4, the midpoint sum is the best of the
three approximations. This is usually the case.
We will denote the three Riemann Sums, with n subintervals, by L(n), R(n),
and M(n). (These sums are also sometimes called “rules.”)

E2. Using Trapezoids

We now find the areas of the strips in Figure N6–6 by using trapezoids. We
denote the bases of the trapezoids by y 0 , y 1 , y 2 , . . ., yn and the heights by Δx =
h 1 , h 2 , . . . , hn.

Figure  N6–6

Trapezoid   Rule

The following sum, denoted T(n), approximates the area between f and the x-axis
from a to b: