Calculating the area under a curve given a set of coordinates, without knowing the function

The numpy and scipy libraries include the composite trapezoidal (numpy.trapz) and Simpson’s (scipy.integrate.simps) rules.

Here’s a simple example. In both trapz and simps, the argument dx=5 indicates that the spacing of the data along the x axis is 5 units.

import numpy as np
from scipy.integrate import simps
from numpy import trapz


# The y values.  A numpy array is used here,
# but a python list could also be used.
y = np.array([5, 20, 4, 18, 19, 18, 7, 4])

# Compute the area using the composite trapezoidal rule.
area = trapz(y, dx=5)
print("area =", area)

# Compute the area using the composite Simpson's rule.
area = simps(y, dx=5)
print("area =", area)

Output:

area = 452.5
area = 460.0