4. Find Solution of an equation 2x^3-4x+1 using Simpson's 1/3 rule
x1 = 2 and x2 = 4
Step value (h) = 0.5

Solution:
Equation is `f(x)=2x^3-4x+1`.

The value of table for `x` and `y`

x	2	2.5	3	3.5	4
y	9	22.25	43	72.75	113

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=0.5/3 [(9 +113)+4xx(22.25+72.75)+2xx(43)]`

`int y dx=0.5/3 [(9 +113)+4xx(95)+2xx(43)]`

`int y dx=0.5/3 [(122)+(380)+(86)]`

`int y dx=98`

Solution by Simpson's `1/3` Rule is `98`

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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=9`

`4y_1=4*22.25=89`

`2y_2=2*43=86`

`4y_3=4*72.75=291`

`y_4=113`

`int y dx=0.5/3*(9+89+86+291+113)`

`int y dx=0.5/3*(588)`

`int y dx=98`

Solution by Simpson's `1/3` Rule is `98`

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