Formula

3. Simpsons `3/8` Rule `int y dx = (3h)/8 (y_0 + 2(y_3 + y_6 + ... + y_(n-3)) + 3(y_1 + y_2 + y_4 + y_5 + ... + y_(n-2)+y_(n-1)) + y_n)`

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Examples
1. Find Solution using Simpson's 3/8 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 Simpson's `3/8` Rule

`int y dx = (3h)/8 [(y_0+y_4) + 2(y_3) + 3(y_1+y_2)]`

`int y dx = (3xx0.2)/8 [(4.0552 + 9.025) + 2xx(7.3891) + 3xx(4.953 + 6.0436)]`

`int y dx = (3xx0.2)/8 [(4.0552 + 9.025) + 2xx(7.3891) + 3xx(10.9966)]`

`int y dx = 4.5636`

Solution by Simpson's `3/8` Rule is `4.5636`

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2. Find Solution using Simpson's 3/8 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 Simpson's `3/8` Rule

`int y dx = (3h)/8 [(y_0+y_4) + 2(y_3) + 3(y_1+y_2)]`

`int y dx = (3xx0.1)/8 [(1 + 0.8604) + 2xx(0.9776) + 3xx(0.9975 + 0.99)]`

`int y dx = (3xx0.1)/8 [(1 + 0.8604) + 2xx(0.9776) + 3xx(1.9875)]`

`int y dx = 0.36668`

Solution by Simpson's `3/8` Rule is `0.36668`

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