MATLAB Function Reference  cumtrapz

Cumulative trapezoidal numerical integration

Syntax

• ```Z = cumtrapz(Y)
Z = cumtrapz(X,Y)
Z = cumtrapz(... dim)
```

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

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:

• ```z = exp(1i*pi*(0:100)/100);

ct = cumtrapz(z,1./z);
ct(end)
ans =
0.0000 + 3.1411i
```

See Also

`cumsum`, `trapz`

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