Page 96 - Calc for the Clueless

This method, the only one of the three that does not actually require calculus, approximates the area under the
curve by trapezoids, by approximating the ''top" of the region by a line.

Divide the region into n equal parts. See the trapezoids. They are standing on their heights. The area of a
trapezoid is ½ h (b 1 + b 2). All of the h's are the same. For the first trapezoid, b 1 = y 1 and b 2 = y 2. A = ½ h (y 1 +
y 2). For the second trapezoid, b 1 = y 2 and b 2 = y 3. A = ½ h (y 2 + y 3).

Notice that the lower base of the first trapezoid is the upper base of the second trapezoid. Every base is doubled
except the first upper base and the last lower base. The formula is A = ½ h (y 0 + 2y 1 + 2y 2 + ... + 2y n - 1 + y n).

Example 9—

Approximate dx using six equal subdivisions.

The interval is of length 4 - 1 = 3.

Six equal, parts? Each h = 3/6 = ½.

Parabolic Method