# trapz

## Purpose

Trapezoidal numerical integration.

## Synopsis

    z = trapz(x,y)
    z = trapz(y)

## Description

`z = trapz(x,y)` computes the integral of `y` with respect to `x` using trapezoidal integration. `x` and `y` must be vectors of the same length, or `x` must be a column vector and `y` a matrix with as many rows as `x`. `trapz` computes the integral of each column of `y` separately. The resulting `z` is a scalar or a row vector.

`z = trapz(y)` computes the trapezoidal integral of `y` assuming unit spacing between the data points. To compute the integral for spacing other than one, multiply `z` by the spacing increment.

## Examples

The exact value of

is 2. To approximate this numerically on a uniformly spaced grid, use

        x = 0:pi/100:pi;
        y = sin(x);

Then both

    z = trapz(x,y)

and

    z = pi/100*trapz(y)

produce

    z =
        1.9998

A nonuniformly spaced example is generated by

    x = sort(rand(1,101)*pi);
    y = sin(x);
    z = trapz(x,y);

The result is not as accurate as the uniformly spaced grid. One random sample produced

    z =
        1.9984

## See Also

    cum, quad, quad8, sum

(c) Copyright 1994 by The MathWorks, Inc.