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Tutorial: Simpson's Rule

Finally, we multiply columns and add up the results:

Step 4: Add the results

Now we need to multiply each function value times the constant in the previous column. In our example, the formula we put in D2 is =C2*B2:

 
A
B
C
D
1
x
f(x)
Constants Product
2
2.00
4.00
1

4

3
2.75
7.56
4
30.25
4
3.50
12.25
2
24.5
5
4.25
18.06
4
72.25
6
5.00
25.00
2
50
7
5.75
33.06
4
132.25
8
6.50
42.25
2
21.13
9
7.25
52.56
4
84.5
10
8.00
64.00
1
210.25
11
    Sum:
168

Finally, we add up everything in the last column with a SUM command, or using the Sum button on the toolbar (see Special Functions in Excel for 2015 for help with this), and multiply by h/3. In this case, we used =(.75/3)*SUM(D2:D10) in D11.

All of this has resulted in the original Simpson's rule formula:

(h/3)[f(x0) + 4f(x1) + 2f(x2) + ... +4f(xn-1) + f(xn)]

 

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