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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

3. Example-3 (table data)
(Previous example)
5. Example-5 (`f(x)=1/(x+1)`)
(Next example)

4. Example-4 (`f(x)=1/x`)





1. Find Solution of an equation 1/x using Trapezoidal rule
x1 = 1 and x2 = 2
Step value (h) = 0.25


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

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

x11.251.51.752
y10.80.66670.57140.5

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

`int y dx=0.25/2 [1 +0.5 + 2xx(0.8+0.6667+0.5714)]`

`int y dx=0.25/2 [1 +0.5 + 2xx(2.0381)]`

`int y dx=0.25/2 [1 +0.5 + 4.0762]`

`int y dx=0.697`

Solution by Trapezoidal Rule is `0.697`



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

`y_0=1`

`2y_1=2*0.8=1.6`

`2y_2=2*0.6667=1.3333`

`2y_3=2*0.5714=1.1429`

`y_4=0.5`

`int y dx=0.25/2*(1+1.6+1.3333+1.1429+0.5)`

`int y dx=0.25/2*(5.5762)`

`int y dx=0.697`

Solution by Trapezoidal Rule is `0.697`




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3. Example-3 (table data)
(Previous example)
5. Example-5 (`f(x)=1/(x+1)`)
(Next example)





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