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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

4. Example-4 (`f(x)=1/x`)
(Previous example)
6. Example-6 (`x^3-2x+1`)
(Next example)

5. Example-5 (`f(x)=1/(x+1)`)





2. Find Solution of an equation 1/(x+1) using Trapezoidal rule
x1 = 0 and x2 = 1
Interval N = 5


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

`h = (b-a)/N`

`h = (1 - 0) / 5 = 0.2`

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

x00.20.40.60.81
y10.83330.71430.6250.55560.5

Method-1:
Using Trapezoidal Rule
`int y dx=h/2 [y_0+y_5+2(y_1+y_2+y_3+y_4)]`

`int y dx=0.2/2 [1 +0.5 + 2xx(0.8333+0.7143+0.625+0.5556)]`

`int y dx=0.2/2 [1 +0.5 + 2xx(2.7282)]`

`int y dx=0.2/2 [1 +0.5 + 5.4563]`

`int y dx=0.6956`

Solution by Trapezoidal Rule is `0.6956`



Method-2:
Using Trapezoidal Rule
`int y dx=h/2 [y_0+2y_1+2y_2+2y_3+2y_4+y_5]`

`y_0=1`

`2y_1=2*0.8333=1.6667`

`2y_2=2*0.7143=1.4286`

`2y_3=2*0.625=1.25`

`2y_4=2*0.5556=1.1111`

`y_5=0.5`

`int y dx=0.2/2*(1+1.6667+1.4286+1.25+1.1111+0.5)`

`int y dx=0.2/2*(6.9563)`

`int y dx=0.6956`

Solution by Trapezoidal Rule is `0.6956`




This material is intended as a summary. Use your textbook for detail explanation.
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4. Example-4 (`f(x)=1/x`)
(Previous example)
6. Example-6 (`x^3-2x+1`)
(Next example)





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