Numerical Integration
Numerical Integration
Numerical Integration
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Simpson’s 1/3 Rule<br />
( x − x1<br />
)( x − x2)<br />
( x − x0)(<br />
x − x2)<br />
f<br />
2<br />
(<br />
x<br />
) =<br />
f<br />
(<br />
x<br />
0<br />
)<br />
+<br />
f<br />
(<br />
x<br />
1<br />
)<br />
+<br />
( x − x )( x − x ) ( x − x )( x − x )<br />
0<br />
1<br />
0<br />
( x −<br />
( x −<br />
2<br />
2<br />
x<br />
x<br />
)( x<br />
)( x<br />
− x1<br />
)<br />
− x )<br />
0 f<br />
(<br />
x2<br />
0 2 1<br />
• After integration ti and algebraic manipulation:<br />
I<br />
h<br />
3<br />
0<br />
1<br />
+<br />
x −<br />
2<br />
x<br />
h = 0<br />
2<br />
≅<br />
[ f<br />
(<br />
x<br />
)<br />
+<br />
4<br />
f<br />
(<br />
x<br />
) +<br />
f<br />
(<br />
x<br />
)<br />
]<br />
© 2003-2006 Roberto Muscedere 19<br />
1<br />
0<br />
)<br />
2<br />
1<br />
2
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