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%matplotlib inline

import matplotlib.pyplot as plt

import scipy.integrate

https://docs.scipy.org/doc/scipy-1.3.0/reference/tutorial/integrate.html
https://docs.scipy.org/doc/scipy-1.3.0/reference/integrate.html

Integrating functions, given callable object (scipy.integrate.quad)

See:

https://docs.scipy.org/doc/scipy-1.3.0/reference/tutorial/integrate.html#general-integration-quad
https://docs.scipy.org/doc/scipy-1.3.0/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad

Example:

$$I = \int_{0}^{3} x^2 dx = \frac{1}{3} 3^3 = 9$$



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f = lambda x: np.power(x, 2)

result = scipy.integrate.quad(f, 0, 3)
result

The return value is a tuple, with the first element holding the estimated value of the integral and the second element holding an upper bound on the error.

Integrating functions, given fixed samples

https://docs.scipy.org/doc/scipy-1.3.0/reference/tutorial/integrate.html#integrating-using-samples



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x = np.linspace(0., 3., 100)
y = f(x)



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plt.plot(x, y);

In case of arbitrary spaced samples, the two functions trapz and simps are available.



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result = scipy.integrate.simps(y, x)
result



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result = scipy.integrate.trapz(y, x)
result