Numerical Integration

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Trapezoidal Rule: Example • Why so bad? © 2003-2006 Roberto Muscedere 8
Trapezoidal Rule • Add a series of intervals b − a = x = a x = b n n h 0 x 1 x 2 x n I = ∫ f + + + ( x ) dx ∫ f ( x ) dx L ∫ f ( x ) dx x 0 x 1 x n− 1 © 2003-2006 Roberto Muscedere 9
Page 1 and 2: Numerical Integration • Newton-Co
Page 3 and 4: Trapezoidal Rule • Trapezoidal Ru
Page 5 and 6: Trapezoidal Rule • Same result if
Page 7: Trapezoidal Rule: Example f (0) = 0
Page 11 and 12: • Grouping the terms: Trapezoidal
Page 13 and 14: Trapezoidal Rule: Example f (0) = 0
Page 15 and 16: Trapezoidal Code (p.2) double Integ
Page 17 and 18: Trapezoidal Code -Output n=1, I=0.1
Page 19 and 20: Simpson’s 1/3 Rule ( x − x1 )(
Page 21 and 22: Simpson’s 1/3 Rule: Example • N
Page 23 and 24: Simpson’s 1/3 Rule • Add a seri
Page 25 and 26: Simpson’s 1/3 Rule • Grouping t
Page 27 and 28: I f Simpson’s 1/3 Rule: Example (
Page 29 and 30: Simpson’s 1/3 Code (p.2) double I
Page 31 and 32: Simpson’s 1/3 Code (p.4) double F

Numerical Integration

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