1. Find Solution of an equation 1/x using Simpson's 1/3 rule
x1 = 1 and x2 = 2
Step value (h) = 0.25

Solution:
Equation is `f(x)=(1)/(x)`.

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

x	1	1.25	1.5	1.75	2
y	1	0.8	0.6667	0.5714	0.5

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=0.25/3 [(1 +0.5)+4xx(0.8+0.5714)+2xx(0.6667)]`

`int y dx=0.25/3 [(1 +0.5)+4xx(1.3714)+2xx(0.6667)]`

`int y dx=0.25/3 [(1.5)+(5.4857)+(1.3333)]`

`int y dx=0.6933`

Solution by Simpson's `1/3` Rule is `0.6933`

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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*0.8=3.2`

`2y_2=2*0.6667=1.3333`

`4y_3=4*0.5714=2.2857`

`y_4=0.5`

`int y dx=0.25/3*(1+3.2+1.3333+2.2857+0.5)`

`int y dx=0.25/3*(8.319)`

`int y dx=0.6933`

Solution by Simpson's `1/3` Rule is `0.6933`

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