How to calculate improper integral in python?

Question

How can I calculate the value of this integral:

f_tu(t) is given as numpy.array. The graph looks like this:

How can I implement this? Everything I could find looks something like this

from scipy.integrate import quad
def f(x):
    return 1/sin(x)
I = quad(f, 0, 1)

but I have an array there, not a specific function like sin.

Answer 1

How about auc from sklearn.metrics?

import numpy as np

import numpy as np

from scipy.integrate import quad

from sklearn.metrics import auc

x = np.arange(0, 100, 0.001)
y = np.sin(x)

print('auc:', auc(x,y))

print('quad:', quad(np.sin, 0, 100))

auc: 0.13818791291277366
quad: (0.1376811277123232, 9.459751315610276e-09)