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

Method-1:
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=0.1/3 [(1.8604)+(7.9004)+(1.98)]`

`int y dx=0.3914`

Solution by Simpson's `1/3` Rule is `0.3914`

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Method-2:
Using Simpsons `1/3` Rule

`int y dx=h/3 [y_0+4y_1+2y_2+4y_3+y_4]`

`y_0=1`

`4y_1=4*0.9975=3.99`

`2y_2=2*0.99=1.98`

`4y_3=4*0.9776=3.9104`

`y_4=0.8604`

`int y dx=0.1/3*(1+3.99+1.98+3.9104+0.8604)`

`int y dx=0.1/3*(11.7408)`

`int y dx=0.3914`

Solution by Simpson's `1/3` Rule is `0.3914`

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