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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

2. Example-2 (table data)
(Previous example)
4. Example-4 (`f(x)=1/x`)
(Next example)

3. Example-3 (table data)





3. Find Solution using Trapezoidal rule
xf(x)
0.001.0000
0.250.9896
0.500.9589
0.750.9089
1.000.8415


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

x00.250.50.751
y10.98960.95890.90890.8415

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 +0.8415 + 2xx(0.9896+0.9589+0.9089)]`

`int y dx=0.25/2 [1 +0.8415 + 2xx(2.8574)]`

`int y dx=0.25/2 [1 +0.8415 + 5.7148]`

`int y dx=0.9445`

Solution by Trapezoidal Rule is `0.9445`



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*0.9896=1.9792`

`2y_2=2*0.9589=1.9178`

`2y_3=2*0.9089=1.8178`

`y_4=0.8415`

`int y dx=0.25/2*(1+1.9792+1.9178+1.8178+0.8415)`

`int y dx=0.25/2*(7.5563)`

`int y dx=0.9445`

Solution by Trapezoidal Rule is `0.9445`




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2. Example-2 (table data)
(Previous example)
4. Example-4 (`f(x)=1/x`)
(Next example)





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