3. Find Solution using Simpson's 3/8 rule

x	f(x)
0.00	1.0000
0.25	0.9896
0.50	0.9589
0.75	0.9089
1.00	0.8415

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

x	0	0.25	0.5	0.75	1
y	1	0.9896	0.9589	0.9089	0.8415

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 +0.8415)+2xx(0.9089)+3xx(0.9896+0.9589)]`

`int y dx=(3xx0.25)/8 [(1 +0.8415)+2xx(0.9089)+3xx(1.9485)]`

`int y dx=(3xx0.25)/8 [(1.8415)+(1.8178)+(5.8455)]`

`int y dx=0.8911`

Solution by Simpson's `3/8` Rule is `0.8911`

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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=1`

`3y_1=3*0.9896=2.9688`

`3y_2=3*0.9589=2.8767`

`2y_3=2*0.9089=1.8178`

`y_4=0.8415`

`int y dx=(3xx0.25)/8 *(1+2.9688+2.8767+1.8178+0.8415)`

`int y dx=(3xx0.25)/8 *(9.5048)`

`int y dx=0.8911`

Solution by Simpson's `3/8` Rule is `0.8911`

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