# numpy.trapz¶

numpy.trapz(y, x=None, dx=1.0, axis=-1)[source]

Integrate along the given axis using the composite trapezoidal rule.

Integrate y (x) along given axis.

Parameters: y : array_like Input array to integrate. x : array_like, optional The sample points corresponding to the y values. If x is None, the sample points are assumed to be evenly spaced dx apart. The default is None. dx : scalar, optional The spacing between sample points when x is None. The default is 1. axis : int, optional The axis along which to integrate. trapz : float Definite integral as approximated by trapezoidal rule.

Notes

Image [R287] illustrates trapezoidal rule – y-axis locations of points will be taken from y array, by default x-axis distances between points will be 1.0, alternatively they can be provided with x array or with dx scalar. Return value will be equal to combined area under the red lines.

References

 [R287] (1, 2) Illustration image: http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png

Examples

```>>> np.trapz([1,2,3])
4.0
>>> np.trapz([1,2,3], x=[4,6,8])
8.0
>>> np.trapz([1,2,3], dx=2)
8.0
>>> a = np.arange(6).reshape(2, 3)
>>> a
array([[0, 1, 2],
[3, 4, 5]])
>>> np.trapz(a, axis=0)
array([ 1.5,  2.5,  3.5])
>>> np.trapz(a, axis=1)
array([ 2.,  8.])
```

numpy.cross

numpy.exp