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4. Boole's rule (Numerical integration) example ( Enter your problem )
  1. Formula & Example-1 (table data)
  2. Example-2 (`f(x)=1/x`)
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

1. Formula & Example-1 (table data)
(Previous example)
5. Weddle's rule
(Next method)

2. Example-2 (`f(x)=1/x`)





1. Find Solution of an equation 1/x using Boole's rule
x1 = 1 and x2 = 2
N = 8


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

`h = (b-a)/N`

`h = (2 - 1) / 8 = 0.125`

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

x11.1251.251.3751.51.6251.751.8752
y10.88890.80.72730.66670.61540.57140.53330.5

Using Boole's Rule
`int y dx = (2h)/45 [7(y_0 + y_8) + 32(y_1+y_3+y_5+y_7) + 12(y_2+y_6) + 14(y_4)]`

`int y dx = (2xx0.125)/45 [7xx(1 + 0.5) + 32xx(0.8889+0.7273+0.6154+0.5333) + 12xx(0.8+0.5714) + 14xx(0.6667)]`

`int y dx = (2xx0.125)/45 [7xx(1.5) + 32xx(2.7649) + 12xx(1.3714) + 14xx(0.6667)]`

`int y dx = 0.6931`

Solution by Boole's Rule is `0.6931`


2. Find Solution of an equation 2x^3-4x+1 using Boole's 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`

x22.533.54
y922.254372.75113

Using Boole's Rule
`int y dx = (2h)/45 [7(y_0 + y_4) + 32(y_1+y_3) + 12(y_2) + 14()]`

`int y dx = (2xx0.5)/45 [7xx(9 + 113) + 32xx(22.25+72.75) + 12xx(43) + 14xx()]`

`int y dx = (2xx0.5)/45 [7xx(122) + 32xx(95) + 12xx(43) + 14xx(0)]`

`int y dx = 98`

Solution by Boole's Rule is `98`


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1. Formula & Example-1 (table data)
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5. Weddle's rule
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