1. Find Solution of an equation 1/x using Simpson's 3/8 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 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=(3xx0.25)/8 [(1 +0.5)+2xx(0.5714)+3xx(0.8+0.6667)]`

`int y dx=(3xx0.25)/8 [(1 +0.5)+2xx(0.5714)+3xx(1.4667)]`

`int y dx=(3xx0.25)/8 [(1.5)+(1.1429)+(4.4)]`

`int y dx=0.6603`

Solution by Simpson's `3/8` Rule is `0.6603`

---

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=1`

`3y_1=3*0.8=2.4`

`3y_2=3*0.6667=2`

`2y_3=2*0.5714=1.1429`

`y_4=0.5`

`int y dx=(3xx0.25)/8 *(1+2.4+2+1.1429+0.5)`

`int y dx=(3xx0.25)/8 *(7.0429)`

`int y dx=0.6603`

Solution by Simpson's `3/8` Rule is `0.6603`

---

---