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Trapezoidal numerical integration

`Q = trapz(`

computes the approximate integral of
`Y`

)`Y`

via the trapezoidal method with unit spacing. The size of
`Y`

determines the dimension to integrate along:

If

`Y`

is a vector, then`trapz(Y)`

is the approximate integral of`Y`

.If

`Y`

is a matrix, then`trapz(Y)`

integrates over each column and returns a row vector of integration values.If

`Y`

is a multidimensional array, then`trapz(Y)`

integrates over the first dimension whose size does not equal 1. The size of this dimension becomes 1, and the sizes of other dimensions remain unchanged.

`Q = trapz(___,`

integrates along the
dimension `dim`

)`dim`

using any of the previous syntaxes. You must
specify `Y`

, and optionally can specify `X`

.
If you specify `X`

, then it can be a scalar or a vector with
length equal to `size(Y,dim)`

. For example, if
`Y`

is a matrix, then `trapz(X,Y,2)`

integrates each row of `Y`

.

Use

`trapz`

and`cumtrapz`

to perform numerical integrations on discrete data sets. Use`integral`

,`integral2`

, or`integral3`

instead if a functional expression for the data is available.`trapz`

reduces the size of the dimension it operates on to 1, and returns only the final integration value.`cumtrapz`

also returns the intermediate integration values, preserving the size of the dimension it operates on.