Trapezoidal rule (Numerical integration) Formula & Example-1 (table data)

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1. Trapezoidal rule (Numerical integration) example ( Enter your problem )

( Enter your problem )

Formula & Example-1 (table data)
Example-2 (`f(x)=1/x`)

Other related methods

2. Example-2 (`f(x)=1/x`)
(Next example)

1. Formula & Example-1 (table data)

Formula

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

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

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 = 4.9852`

Solution by Trapezoidal Rule is `4.9852`

2. Find Solution using Trapezoidal rule
x f(x)
0.0 1.0000
0.1 0.9975
0.2 0.9900
0.3 0.9776
0.4 0.8604

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

x	0	0.1	0.2	0.3	0.4
y	1	0.9975	0.99	0.9776	0.8604

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 = 0.38953`

Solution by Trapezoidal Rule is `0.38953`

This material is intended as a summary. Use your textbook for detail explanation.
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