ABSTRACT
Now, de›ne = ( )f f xi i . Solving Equation (5.2) for fi, +1fi , and −1fi gives
= =
= = + +
= = − + − +
( )
( ) ( )
( ) ( ) ( )
f x f c
f x f a x b x c
f x f a x b x c
Adding the last two equations gives + = ++ − 2 21 1 2f f a x ci i . Solving for a gives
= + −+ −
1 2
[ 2 ]2 1 1a x f f fi i i
en,
= × + − + = + − ++ − + −
2 3
1 2
[ 2 ]( ) 2 3
1 1A x f f f x f x
or
= + +
x f f fi i i (5.4)
To obtain an approximation for the integral I, we need to sum all the two-strip areas under the curve from x = A to x = B (see Figure 5.2), that is,
= + +
= + +
= + +
= + + − +
3 [ 4 ]
3 [ 4 ]
3 [ 4 ]
3 [ 4 ]
A x
f f f
A x
f f f
A x
f f f
A x
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us,
∫= = + + + + + + + =
( ) 3
[ 4 2 4 2 4 ]1 2 3 4 5 1 1
I f x dx x
f f f f f f f x A
(5.5)
is is Simpson’s rule for integration.
