Notice how each trapezoid shares a base with the trapezoid next to it, except for the end ones. This
enables us to simplify the formula for using the Trapezoid Rule. Each trapezoid has a height equal to the
length of the interval divided by the number of trapezoids we use. If the interval is from x = a to x = b, and
the number of trapezoids is n, then the height of each trapezoid is . Then our formula is
[y 0 + 2y 1 + 2y 2 + 2y 3 ...+ 2yn (^) − 2 + 2yn]This is all you need to know about the Trapezoid Rule. Just follow the formula, and you won’t have any
problems. Let’s do one more example.
Example 10: Approximate the area under the curve y = x^3 from x = 2 to x = 3 using four inscribed
trapezoids.
Following the rule, the height of each trapezoid is . Thus, the approximate area is
Compare this answer to the actual value we found earlier—it’s pretty close!
PROBLEM 1. Approximate the area under the curve y = 4 − x^2 from x = −1 to x = 1 with n = 4 inscribed
rectangles.
Answer: Draw four rectangles that look like this.