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Tutorial: Simpson's Rule

Now we need our constants, which follow the pattern 1, 4, 2, 4, 2, ..., 4, 2, 4, 1.

Step 3: Add the constant column

Now add a third column in the pattern of the constants for Simpson's rule: the first row should have a 1, the second four, then two, alternating between four and two until you reach the last row which should be a 1:

 
A
B
C
1
x
f(x)
Constants
2
2.00
4.00
1
3
2.75
7.56
4
4
3.50
12.25
2
5
4.25
18.06
4
6
5.00
25.00
2
7
5.75
33.06
4
8
6.50
42.25
2
9
7.25
52.56
4
10
8.00
64.00
1

Hint: The next to the last row should have a four again. If it doesn't, you have made a mistake somewhere. (Did you remember to use an even n?)

Finally, we're ready to multiply out and add.

 

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