# scipy.integrate.cumulative_trapezoid

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

  Cumulatively integrate y(x) using the composite trapezoidal rule.

  Parameters:
    y array_like

      Values to integrate.

    x array_like, optional

      The coordinate to integrate along. If None (default), use spacing dx between consecutive elements in y.

    dx float, optional

      Spacing between elements of y. Only used if x is None.

    axis int, optional

      Specifies the axis to cumulate. Default is -1 (last axis).

    initial scalar, optional

      If given, insert this value at the beginning of the returned result. Typically this value should be 0. Default is None, which means no value at `x[0]` is returned and res has one element less than y along the axis of integration.

  Returns:
    res ndarray

      The result of cumulative integration of y along axis. If initial is None, the shape is such that the axis of integration has one less value than y. If initial is given, the shape is equal to that of y.

  See also

  `numpy.cumsum`, `numpy.cumprod`
  `quad`

    adaptive quadrature using QUADPACK

  `romberg`

    adaptive Romberg quadrature

  `quadrature`

    adaptive Gaussian quadrature

  `fixed_quad`

    fixed-order Gaussian quadrature

  `dblquad`

    double integrals

  `tplquad`

    triple integrals

  `romb`

    integrators for sampled data

  `ode`

    ODE integrators

  `odeint`

    ODE integrators

  Examples

      >>> from scipy import integrate
      >>> import numpy as np
      >>> import matplotlib.pyplot as plt

      >>> x = np.linspace(-2, 2, num=20)
      >>> y = x
      >>> y_int = integrate.cumulative_trapezoid(y, x, initial=0)
      >>> plt.plot(x, y_int, 'ro', x, y[0] + 0.5 * x**2, 'b-')
      >>> plt.show()