Formula
1. Boole's Rule
`int y dx =(2h)/45 [7(y_0 + y_n) + 32(y_1+y_3+y_5+...) + 12(y_2+y_6+y_10+...) + 14(y_4+y_8+y_12+...)]`
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Examples
1. Find Solution using Boole's 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 |
|---|
Using Boole's Rule
`int y dx = (2h)/45 [7(y_0 + y_4) + 32(y_1+y_3) + 12(y_2) + 14()]`
`int y dx = (2xx0.2)/45 [7xx(4.0552 + 9.025) + 32xx(4.953+7.3891) + 12xx(6.0436) + 14xx()]`
`int y dx = (2xx0.2)/45 [7xx(13.0802) + 32xx(12.3421) + 12xx(6.0436) + 14xx(0)]`
`int y dx = 4.9692`
Solution by Boole's Rule is `4.9692`
2. Find Solution using Boole's 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 |
|---|
Using Boole's Rule
`int y dx = (2h)/45 [7(y_0 + y_4) + 32(y_1+y_3) + 12(y_2) + 14()]`
`int y dx = (2xx0.1)/45 [7xx(1 + 0.8604) + 32xx(0.9975+0.9776) + 12xx(0.99) + 14xx()]`
`int y dx = (2xx0.1)/45 [7xx(1.8604) + 32xx(1.9751) + 12xx(0.99) + 14xx(0)]`
`int y dx = 0.39158`
Solution by Boole's Rule is `0.39158`
This material is intended as a summary. Use your textbook for detail explanation.
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