Formula
2. Simpsons `1/3` Rule
`int y dx = h/3 (y_0 + 4(y_1 + y_3 + y_5 + ... + + y_(n-1)) + 2(y_2 + y_4 + y_6 + ... + y_(n-2)) + y_n)`
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Examples
1. Find Solution using Simpson's 1/3 rule
| x | f(x) |
| 1.4 | 4.0552 |
| 1.6 | 4.9530 |
| 1.8 | 6.0436 |
| 2.0 | 7.3891 |
| 2.2 | 9.0250 |
Solution:
The value of table for `x` and `y`
| x | 1.4 | 1.6 | 1.8 | 2 | 2.2 |
|---|
| y | 4.0552 | 4.953 | 6.0436 | 7.3891 | 9.025 |
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Using Simpsons `1/3` Rule
`int y dx = h/3 [(y_0 + y_4) + 4(y_1 + y_3) + 2(y_2)]`
`int y dx = 0.2/3 [(4.0552 + 9.025) + 4xx(4.953 + 7.3891) + 2xx(6.0436)]`
`int y dx = 0.2/3 [(4.0552 + 9.025) + 4xx(12.3421) + 2xx(6.0436)]`
`int y dx = 4.9691`
Solution by Simpson's `1/3` Rule is `4.9691`
2. Find Solution using Simpson's 1/3 rule
| x | f(x) |
| 0.0 | 1.0000 |
| 0.1 | 0.9975 |
| 0.2 | 0.9900 |
| 0.3 | 0.9776 |
| 0.4 | 0.8604 |
Solution:
The value of table for `x` and `y`
| x | 0 | 0.1 | 0.2 | 0.3 | 0.4 |
|---|
| y | 1 | 0.9975 | 0.99 | 0.9776 | 0.8604 |
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Using Simpsons `1/3` Rule
`int y dx = h/3 [(y_0 + y_4) + 4(y_1 + y_3) + 2(y_2)]`
`int y dx = 0.1/3 [(1 + 0.8604) + 4xx(0.9975 + 0.9776) + 2xx(0.99)]`
`int y dx = 0.1/3 [(1 + 0.8604) + 4xx(1.9751) + 2xx(0.99)]`
`int y dx = 0.39136`
Solution by Simpson's `1/3` Rule is `0.39136`
This material is intended as a summary. Use your textbook for detail explanation.
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