Numerical Integration

# Numerical Integration - Numerical Integration Numerical...

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Numerical Integration Numerical Integration Section 4.6

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Some elementary functions don’t have antiderivatives that are elementary functions. Trapezoids approximate the area better than rectangles in most cases. 1 3 - x x x x cos x 3 1 -
Area of trapezoid = ½ h( b 1 + b 2 ) Area of i th trapezoid = f (x i-1 )+f(x i ) b – a 2 n x 0 x 1 x 2 x 3

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b – a f(x 0 ) + f(x 1 ) + f(x 1 ) + f(x 2 )+ n 2 2 ……. f (x n-1 ) + f(x n ) 2
Thm. 4.16 The Trapezoidal Thm. 4.16 The Trapezoidal Rule Rule Let f be continuous on [a, b]. f (x)dx b a 2n b - a [ f(x 0 ) + 2f(x 1 ) + 2f(x 2 ) + …… + 2f(x n-1 ) + f(x n

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Numerical Integration - Numerical Integration Numerical...

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