(a)
.Example 25 __
Use T(4) to approximate .
SOLUTION: From Example 24, . 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.SOLUTION: Note that the subinterval widths are not equal.
In each subinterval, we sketch the rectangle with height determined by the
point on f at the left endpoint. Our estimate is the sum of the areas of these
rectangles: