Home > Numerical methods calculators > Numerical Integration using Trapezoidal Rule example

1. Trapezoidal 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 Trapezoidal 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 Trapezoidal Rule
`int y dx=h/2 [y_0+y_4+2(y_1+y_2+y_3)]`

`int y dx=0.5/2 [5 +57 + 2xx(11.625+22+36.875)]`

`int y dx=0.5/2 [5 +57 + 2xx(70.5)]`

`int y dx=0.5/2 [5 +57 + 141]`

`int y dx=50.75`

Solution by Trapezoidal Rule is `50.75`



Method-2:
Using Trapezoidal Rule
`int y dx=h/2 [y_0+2y_1+2y_2+2y_3+y_4]`

`y_0=5`

`2y_1=2*11.625=23.25`

`2y_2=2*22=44`

`2y_3=2*36.875=73.75`

`y_4=57`

`int y dx=0.5/2*(5+23.25+44+73.75+57)`

`int y dx=0.5/2*(203)`

`int y dx=50.75`

Solution by Trapezoidal Rule is `50.75`




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
 
 

.