4. Find Solution of an equation 2x^3-4x+1 using Simpson's 3/8 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 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=(3xx0.5)/8 [(9 +113)+2xx(72.75)+3xx(22.25+43)]`

`int y dx=(3xx0.5)/8 [(9 +113)+2xx(72.75)+3xx(65.25)]`

`int y dx=(3xx0.5)/8 [(122)+(145.5)+(195.75)]`

`int y dx=86.8594`

Solution by Simpson's `3/8` Rule is `86.8594`

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Method-2:
Using Simpson's `3/8` Rule

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

`y_0=9`

`3y_1=3*22.25=66.75`

`3y_2=3*43=129`

`2y_3=2*72.75=145.5`

`y_4=113`

`int y dx=(3xx0.5)/8 *(9+66.75+129+145.5+113)`

`int y dx=(3xx0.5)/8 *(463.25)`

`int y dx=86.8594`

Solution by Simpson's `3/8` Rule is `86.8594`

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