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4. Boole'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 (`x^3-2x+1`)
  7. Example-7 (`2x^3-4x+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

6. Example-6 (`x^3-2x+1`)
(Previous example)
5. Weddle's rule
(Next method)

7. Example-7 (`2x^3-4x+1`)





4. 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

Method-1:
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=(2xx0.5)/45 [(854) + (3040) + (516) + (0)]`

`int y dx=98`

Solution by Boole's Rule is `98`



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

`7y_0=7*9=63`

`32y_1=32*22.25=712`

`12y_2=12*43=516`

`32y_3=32*72.75=2328`

`7y_4=7*113=791`

`int y dx=(2xx0.5)/45*(63+712+516+2328+791)`

`int y dx=(2xx0.5)/45*(4410)`

`int y dx=98`

Solution by Boole's Rule is `98`




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6. Example-6 (`x^3-2x+1`)
(Previous example)
5. Weddle's rule
(Next method)





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