Barrons AP Calculus - David Bock

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
The following sum approximates the area between f and the x-axis from a to b:

If all subintervals are of equal width, h, we can remove the common factor

Trapezoid Rule

Using T(n) to denote the approximating sum with n equal subintervals, we have the Trapezoid Rule:

EXAMPLE 25

Use T(4) to approximate

SOLUTION: From Example Then,

This is better than either L(4) or R(4), but M(4) is the best approximation here.

EXAMPLE 26

A function f passes through the five points shown. Estimate the area using (a) a left

rectangular approximation and

(b) a trapezoidal approximation.