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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

6. Example-6 (`x^3-2x+1`)
(Previous example)
2. Simpson's 1/3 rule
(Next method)

7. Example-7 (`2x^3-4x+1`)





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


Solution:
Equation is `f(x)=2x^3-4x+1`.

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

x22.533.54
y922.254372.75113

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 [9 +113 + 2xx(22.25+43+72.75)]`

`int y dx=0.5/2 [9 +113 + 2xx(138)]`

`int y dx=0.5/2 [9 +113 + 276]`

`int y dx=99.5`

Solution by Trapezoidal Rule is `99.5`



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

`y_0=9`

`2y_1=2*22.25=44.5`

`2y_2=2*43=86`

`2y_3=2*72.75=145.5`

`y_4=113`

`int y dx=0.5/2*(9+44.5+86+145.5+113)`

`int y dx=0.5/2*(398)`

`int y dx=99.5`

Solution by Trapezoidal Rule is `99.5`




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6. Example-6 (`x^3-2x+1`)
(Previous example)
2. Simpson's 1/3 rule
(Next method)





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