Integration Rules

Integration Rules - ê ê ù ú ú In both of the above...

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Integration Rules: I. To approximate the integral b a dx x f ) ( using a A. Single Application of the Trapezoid Rule [ ] ) ( ) ( 2 ) ( b f a f a b I T + - = B. Single Application of Simpson’s (1/3) Rule + + + - = ) ( 2 ) ( 6 ) ( b f b a f a f a b I S II. To approximate the integral b a dx x f ) ( using a A. Composite Trapezoid Rule + + = - = ) ( ) ( 2 ) ( 2 1 1 0 N N i i T x f x f x f h I B. Composite Simpson’s Rule I S = h 3 f ( x 0 ) + 4 f ( x 2 i - 1 i =1 N 2 å ) + 2 f ( x 2 i i =1 N - 2 2 å ) + f ( x N ) é
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Unformatted text preview: ë ê ê ù û ú ú In both of the above, N = number of subdivisions (If the independent values (the x’s) are numbered from zero then they run from x to x N .) The spacing between “x” values is h , in these cases kept constant, which is defined as N a b h-= and b x a x N ≡ ≡ and...
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