Skip to main content
`Ctrl`+`K`
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:
    funccallable

      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))`.

    afloat

      Lower limit of integration.

    bfloat

      Upper limit of integration.

    argstuple, optional

      Extra arguments to pass to function, if any.

    nint, optional

      Order of quadrature integration. Default is 5.

  Returns:
    valfloat

      Gaussian quadrature approximation to the integral

    noneNone

      Statically returned value of None

  See also

  `quad`

    adaptive quadrature using QUADPACK

  `dblquad`

    double integrals

  `tplquad`

    triple integrals

  `romb`

    integrators for sampled data

  `simpson`

    integrators for sampled data

  `cumulative_trapezoid`

    cumulative integration for sampled data

  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