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

Method-1:
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=(2xx0.2)/45 [(91.5614) + (394.9472) + (72.5232) + (0)]`

`int y dx=4.9692`

Solution by Boole's Rule is `4.9692`

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Method-2:
Using Boole's Rule
`int y dx=(2h)/45 [7y_0+32y_1+12y_2+32y_3+7y_4]`

`7y_0=7*4.0552=28.3864`

`32y_1=32*4.953=158.496`

`12y_2=12*6.0436=72.5232`

`32y_3=32*7.3891=236.4512`

`7y_4=7*9.025=63.175`

`int y dx=(2xx0.2)/45*(28.3864+158.496+72.5232+236.4512+63.175)`

`int y dx=(2xx0.2)/45*(559.0318)`

`int y dx=4.9692`

Solution by Boole's Rule is `4.9692`

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