# AREA

## Purpose:

Calculates the area of a series, or portion
of a series, using Simpson's Rule.

## Syntax:

AREA(series, start,
length)

series |
- |
Optional. Any series or expression evaluating
to a series. Defaults to the current Window. |

start |
- |
Optional. An integer. The index of the point
defined as the start of the section to for the area calculation. Defaults
to 1, the first point. |

length |
- |
Optional. An integer. The length of the section;
only valid if start has been specified. Defaults to the length of the
section from the start point to the last value of the series. |

## Returns:

A scalar.

## Example:

area(gsin(1000, 1/1000, 0.5))

returns 0.636618.
For a sinusoid, the analytic computation is as follows:

With f = 0.5 and t = 1:

## Example:

y1 = gnorm(1000, .001);

a1 = integ(y1);

a2 = area(y1);

Series
a1 contains the cumulative area of y1
and scalar a2 contains the value
of the total area of y1. Note
that a1[end] == a2, the last point
of the cumulative area equals the total area.

## Remarks:

AREA returns the total area of a series
using the composite Simpson’s rule. This method fits a quadratic polynomial
to three points of the series and performs polynomial integration. In
particular:

where

See INTEG
to return the running or cumulative area of a series.

See TRAPZ
to compute the area using the trapezoidal rule.

See CAREA
to compute the closed loop area of a series.

See POLYAREA
to compute the area of a regular closed polygon.

The area will be calculated correctly
even if the defined start or length require points beyond the end of the
series.

The area below the origin on the y-axis
is negative area. To include the area below y=0 as positive area, take
the absolute value of the series first, e.g. area(abs(W1)).

## See Also:

ABS

CAREA

CUMTRAPZ

INTEG

POLYAREA

TRAPZ