Home > Numerical methods calculators > Numerical Integration using Boole's Rule example

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

5. Example-5 (`f(x)=1/(x+1)`)
(Previous example)
7. Example-7 (`2x^3-4x+1`)
(Next example)

6. Example-6 (`x^3-2x+1`)





3. Find Solution of an equation x^3-2x+1 using Boole's rule
x1 = 2 and x2 = 4
Step value (h) = 0.5


Solution:
Equation is `f(x)=x^3-2x+1`.

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

x22.533.54
y511.6252236.87557

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(5 +57)+32xx(11.625+36.875)+12xx(22)+14xx()]`

`int y dx=(2xx0.5)/45 [7xx(62) + 32xx(48.5) + 12xx(22) + 14xx(0)]`

`int y dx=(2xx0.5)/45 [(434) + (1552) + (264) + (0)]`

`int y dx=50`

Solution by Boole's Rule is `50`



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

`7y_0=7*5=35`

`32y_1=32*11.625=372`

`12y_2=12*22=264`

`32y_3=32*36.875=1180`

`7y_4=7*57=399`

`int y dx=(2xx0.5)/45*(35+372+264+1180+399)`

`int y dx=(2xx0.5)/45*(2250)`

`int y dx=50`

Solution by Boole's Rule is `50`




This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here



5. Example-5 (`f(x)=1/(x+1)`)
(Previous example)
7. Example-7 (`2x^3-4x+1`)
(Next example)





Share this solution or page with your friends.
 
 
Copyright © 2025. All rights reserved. Terms, Privacy
 
 

.