# scipy.integrate.fixed_quad

scipy.integrate.fixed_quad(func, a, b, args=(), n=5)

  Compute a definite integral using fixed-order Gaussian quadrature.

  Integrate func from a to b using Gaussian quadrature of order n.

  Parameters:
    func callable

      A Python function or method to integrate (must accept vector inputs). If integrating a vector-valued function, the returned array must have shape `(..., len(x))`.

    a float

      Lower limit of integration.

    b float

      Upper limit of integration.

    args tuple, optional

      Extra arguments to pass to function, if any.

    n int, optional

      Order of quadrature integration. Default is 5.

  Returns:
    val float

      Gaussian quadrature approximation to the integral

    none None

      Statically returned value of None

  See also

  `quad`

    adaptive quadrature using QUADPACK

  `dblquad`

    double integrals

  `tplquad`

    triple integrals

  `romberg`

    adaptive Romberg quadrature

  `quadrature`

    adaptive Gaussian quadrature

  `romb`

    integrators for sampled data

  `simpson`

    integrators for sampled data

  `cumulative_trapezoid`

    cumulative integration for sampled data

  `ode`

    ODE integrator

  `odeint`

    ODE integrator

  Examples

      >>> from scipy import integrate
      >>> import numpy as np
      >>> f = lambda x: x**8
      >>> integrate.fixed_quad(f, 0.0, 1.0, n=4)
      (0.1110884353741496, None)
      >>> integrate.fixed_quad(f, 0.0, 1.0, n=5)
      (0.11111111111111102, None)
      >>> print(1/9.0)  # analytical result
      0.1111111111111111

      >>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=4)
      (0.9999999771971152, None)
      >>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=5)
      (1.000000000039565, None)
      >>> np.sin(np.pi/2)-np.sin(0)  # analytical result
      1.0