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4.6 Numerical Integration

4.6 Numerical Integration. Trapezoidal Rule. Area of a Trapezoid. b 2. h. b 1. b 1 b 2. h. 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. b.

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4.6 Numerical Integration

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  1. 4.6 Numerical Integration Trapezoidal Rule Area of a Trapezoid b2 h b1 b1 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. b a h x0 x1 x2 x3 x4 simplified to

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

  4. Use the Trapezoidal Rule to approximate 1

  5. Simpson’s Rule n is even Note: The coefficients in Simpson’s Rule have the following pattern 1 4 2 4 2 4 … 4 2 4 2 4 1

  6. Ex. Let n = 4 0 if n = 8

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