The
INT_TABULATED function
integrates a tabulated set of data { *
xi*
, *
fi*
} on the closed interval [MIN(*
x*
) , MAX(*
x*
)], using a five-point
Newton-Cotes integration formula.

**CAUTION: **
Data that is highly oscillatory requires a sufficient number of samples for an accurate integral approximation.

This routine is written in the IDL language. Its source code can be found in the file ```
int_tabulated.pro
```

in the ```
lib
```

subdirectory of the IDL distribution.

Define 11 *
x*
-values on the closed interval [0.0 , 0.8]:

X = [0.0, .12, .22, .32, .36, .40, .44, .54, .64, .70, .80]

Define 11 *
f*
-values corresponding to *
xi*
:

F = [0.200000, 1.30973, 1.30524, 1.74339, 2.07490, 2.45600, $

2.84299, 3.50730, 3.18194, 2.36302, 0.231964]

result = INT_TABULATED(X, F) Integrate.

In this example, the f-values are generated from a known function

*
f*
= 0.2 + 25*
x*
- 200*
x*
^{
2}
+ 675*
x*
^{
3}
- 900*
x*
^{
4}
+ 400*
x*
^{
5}

which allows the determination of an exact solution. A comparison of methods yields the following results: