MATLAB Function Reference |

Trapezoidal numerical integration

**Syntax**

**Description**

```
Z = trapz(Y)
```

computes an approximation of the integral of `Y`

via the trapezoidal method (with unit spacing). To compute the integral for spacing other than one, multiply `Z`

by the spacing increment. Input `Y`

can be complex.

If `Y`

is a vector, `trapz(Y)`

is the integral of `Y`

.

If `Y`

is a matrix,`trapz(Y)`

is a row vector with the integral over each column.

If `Y`

is a multidimensional array, `trapz(Y)`

works across the first nonsingleton dimension.

```
Z = trapz(X,Y)
```

computes the integral of `Y`

with respect to `X`

using trapezoidal integration. Inputs `X`

and `Y`

can be complex.

If `X`

is a column vector and `Y`

an array whose first nonsingleton dimension is `length(X)`

, `trapz(X,Y)`

operates across this dimension.

```
Z = trapz(...,dim)
```

integrates across the dimension of `Y`

specified by scalar `dim`

. The length of `X`

, if given, must be the same as `size(Y,dim)`

.

**Example 1**

To approximate this numerically on a uniformly spaced grid, use

**Example 2**

A nonuniformly spaced example is generated by

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

**Example 3**

This example uses two complex inputs:

**See Also**

trace | treelayout |

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