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5. Weddle's rule (Numerical integration) example ( Enter your problem )
  1. Formula & Example-1 (table data)
  2. Example-2 (table data)
  3. Example-3 (table data)
  4. Example-4 (`f(x)=1/x`)
  5. Example-5 (`f(x)=1/(x+1)`)
  6. Example-6 (`1/(x+1)^2`)
  7. Example-7 (`1/(x+1)`)
Other related methods
  1. Trapezoidal rule
  2. Simpson's 1/3 rule
  3. Simpson's 3/8 rule
  4. Boole's rule
  5. Weddle's rule

4. Boole's rule
(Previous method)
2. Example-2 (table data)
(Next example)

1. Formula & Example-1 (table data)





Formula
1. Weddle's Rule
`int y dx = (3h)/10 [(y_0+5y_1+y_2+6y_3+y_4+5y_5+y_6)+(y_6+5y_7+y_8+6y_9+y_10+5y_11+y_12)+...]`

Examples
1. Find Solution using Weddle's rule
xf(x)
7.471.93
7.481.95
7.491.98
7.502.01
7.512.03
7.522.06
7.532.09


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

x7.477.487.497.57.517.527.53
y1.931.951.982.012.032.062.09

Method-1:
Using Weddle's Rule
`int y dx=(3h)/10 [(y_0+5y_1+y_2+6y_3+y_4+5y_5+y_6)]`

`int y dx=(3xx0.01)/10 [(1.93 + 5xx1.95 + 1.98 + 6xx2.01 + 2.03 + 5xx2.06 + 2.09)]`

`int y dx=(3xx0.01)/10 [40.14]`

`int y dx=0.1204`

Solution by Weddle's Rule is `0.1204`



Method-2:
Using Weddle's Rule
`int y dx=(3h)/10 [(y_0+5y_1+y_2+6y_3+y_4+5y_5+y_6)]`

`y_0=1.93`

`5y_1=5*1.95=9.75`

`y_2=1.98`

`6y_3=6*2.01=12.06`

`y_4=2.03`

`5y_5=5*2.06=10.3`

`y_6=2.09`

`int y dx=(3xx0.01)/10*[(1.93+9.75+1.98+12.06+2.0310.3+2.09)]`

`int y dx=(3xx0.01)/10*(40.14)`

`int y dx=0.1204`

Solution by Weddle's Rule is `0.1204`




This material is intended as a summary. Use your textbook for detail explanation.
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4. Boole's rule
(Previous method)
2. Example-2 (table data)
(Next example)





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