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**Numerical Integration**

4.6 Numerical Integration Trapezoidal Rule Area of a Trapezoid b2 h b1 b b2 h

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We are going to sum up n trapezoids from a to b. Let’s let n = 4 (4 trapezoids) Now we need to find the sums of the area of these four trapezoids. a h b x x1 x x x4 simplified to

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**The bigger n you use, the more accurate your answer**

will be.

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**Use the Trapezoidal Rule to approximate**

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**1 4 2 4 2 4 … 4 2 4 2 4 1 Simpson’s Rule n is even**

Note: The coefficients in Simpson’s Rule have the following pattern …

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Ex. Let n = 4 if n = 8

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