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 |
|---|
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 = 0.6933`
Solution by Simpson's `1/3` Rule is `0.6933`
2. 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 |
|---|
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 = 98`
Solution by Simpson's `1/3` Rule is `98`
This material is intended as a summary. Use your textbook for detail explanation.
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