# scipy.integrate.trapezoid

scipy.integrate.trapezoid(y, x=None, dx=1.0, axis=- 1)

  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.

  Returns
    trapz float

      Definite integral as approximated by trapezoidal rule.

  See also

  `numpy.cumsum`

  Notes

  Image [2] 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

  1

    Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule

  2

    Illustration image: https://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.])

scipy.integrate.AccuracyWarning scipy.integrate.cumulative_trapezoid