1. 6.5 Trapezoidal Rule and Simpson’s Rule Day 1

2. Vocab/Formulas
Trapezoidal Rule: Use trapezoids rather than rectangles to more accurately approximate areas
Area of a Trapezoid:

3. Vocab/Formulas

4. Example 1: Estimate the area under the curve using the trapezoidal rule with four partitions. Is this an overestimation or underestimation? How do you know?

5. Vocab/Formulas
Simpson’s Rule: another approximation of area under the curve; must be divided into an even number of partitions.
Greeks used parabolic arcs to determine this formula to be even more accurate than rectangles or trapezoids
The only reason Simpson got credit for this rule (he did not discover it!) is because he mentioned it in one of his books…just like Pythagoras and Pythagorean Theorem.

6. Example 2: Use Simpson’s Rule with n=4 to approximate

7. Pg. 315 Quick Review 1-9odd EX 1,3,5 Special Focus FTC Worksheet
Assignment
Pg. 315 Quick Review 1-9odd EX 1,3,5 Special Focus FTC Worksheet