MATLAB Function Reference |

Cumulative trapezoidal numerical integration

**Syntax**

**Description**

```
Z = cumtrapz(Y)
```

computes an approximation of the cumulative integral of `Y`

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

by the spacing increment. Input `Y`

can be complex.

For vectors, `cumtrapz(Y)`

is a vector containing the cumulative integral of `Y`

.

For matrices, `cumtrapz(Y)`

is a matrix the same size as `Y`

with the cumulative integral over each column.

For multidimensional arrays, `cumtrapz(Y)`

works across the first nonsingleton dimension.

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

computes the cumulative 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`

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

. `cumtrapz`

operates across this dimension. Inputs `X`

and `Y`

can be complex.

If `X`

is a column vector and `Y`

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

, `cumtrapz(X,Y)`

operates across this dimension.

```
Z = cumtrapz(X,Y,dim) or cumtrapz(Y,dim)
```

integrates across the dimension of `Y`

specified by scalar `dim`

. The length of `X`

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

.

**Example 1**

Y = [0 1 2; 3 4 5]; cumtrapz(Y,1) ans = 0 0 0 1.5000 2.5000 3.5000 cumtrapz(Y,2) ans = 0 0.5000 2.0000 0 3.5000 8.0000

**Example 2**

This example uses two complex inputs:

**See Also **

cumsum | curl |

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