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Numerical Integration

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Presentation on theme: "Numerical Integration"— Presentation transcript:

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

2 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

3 The bigger n you use, the more accurate your answer
will be.

4 Use the Trapezoidal Rule to approximate

5 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

6 Ex. Let n = 4 if n = 8

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