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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

1. Formula & Example-1 (table data)
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3. Example-3 (table data)
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2. Example-2 (table data)





2. Find Solution using Trapezoidal rule
xf(x)
0.01.0000
0.10.9975
0.20.9900
0.30.9776
0.40.8604


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

x00.10.20.30.4
y10.99750.990.97760.8604

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

`int y dx=0.1/2 [1 +0.8604 + 2xx(0.9975+0.99+0.9776)]`

`int y dx=0.1/2 [1 +0.8604 + 2xx(2.9651)]`

`int y dx=0.1/2 [1 +0.8604 + 5.9302]`

`int y dx=0.3895`

Solution by Trapezoidal Rule is `0.3895`



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*0.9975=1.995`

`2y_2=2*0.99=1.98`

`2y_3=2*0.9776=1.9552`

`y_4=0.8604`

`int y dx=0.1/2*(1+1.995+1.98+1.9552+0.8604)`

`int y dx=0.1/2*(7.7906)`

`int y dx=0.3895`

Solution by Trapezoidal Rule is `0.3895`




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