6.5 Trapezoidal Rule and Simpson’s Rule Day 1

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Presentation transcript:

6.5 Trapezoidal Rule and Simpson’s Rule Day 1

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

Vocab/Formulas

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?

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.

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

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