Formula

1. Trapezoidal Rule `int y dx = h/2 (y_0 + 2 (y_1 + y_2 + y_3 + ... + y_(n-1)) + y_n)`

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Examples
1. Find Solution using Trapezoidal rule

x	f(x)
1.4	4.0552
1.6	4.9530
1.8	6.0436
2.0	7.3891
2.2	9.0250

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

x	1.4	1.6	1.8	2	2.2
y	4.0552	4.953	6.0436	7.3891	9.025

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

`int y dx=0.2/2 [4.0552 +9.025 + 2xx(4.953+6.0436+7.3891)]`

`int y dx=0.2/2 [4.0552 +9.025 + 2xx(18.3857)]`

`int y dx=0.2/2 [4.0552 +9.025 + 36.7714]`

`int y dx=4.9852`

Solution by Trapezoidal Rule is `4.9852`

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

`y_0=4.0552`

`2y_1=2*4.953=9.906`

`2y_2=2*6.0436=12.0872`

`2y_3=2*7.3891=14.7782`

`y_4=9.025`

`int y dx=0.2/2*(4.0552+9.906+12.0872+14.7782+9.025)`

`int y dx=0.2/2*(49.8516)`

`int y dx=4.9852`

Solution by Trapezoidal Rule is `4.9852`

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