`scipy.interpolate._bsplines:BSpline.integrate`

Signature

def integrate(self, a, b, extrapolate = None)

Compute a definite integral of the spline.

a : float: Lower limit of integration.
b : float: Upper limit of integration.
extrapolate : bool or 'periodic', optional: whether to extrapolate beyond the base interval, t[k] .. t[-k-1], or take the spline to be zero outside of the base interval. If 'periodic', periodic extrapolation is used. If None (default), use self.extrapolate.

I : array_like: Definite integral of the spline over the interval [a, b].

Construct the linear spline ``x if x < 1 else 2 - x`` on the base interval :math:`[0, 2]`, and integrate it

from scipy.interpolate import BSpline
b = BSpline.basis_element([0, 1, 2])
b.integrate(0, 1)

✓

array(0.5)

If the integration limits are outside of the base interval, the result is controlled by the `extrapolate` parameter

b.integrate(-1, 1)

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array(0.)

b.integrate(-1, 1, extrapolate=False)

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array(0.5)

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.grid(True)

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ax.axvline(0, c='r', lw=5, alpha=0.5)  # base interval
ax.axvline(2, c='r', lw=5, alpha=0.5)

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<matplotlib.lines.Line2D object at 0x7f3f43050590>

xx = [-1, 1, 2]

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ax.plot(xx, b(xx))

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[<matplotlib.lines.Line2D object at 0x7f3f43050980>]

plt.show()

✓