how to integrate a composite function using scipy

Question

I have two functions defined as integrals where the lower and upper limits are (0-1) and (0-10), respectively. I found out the scipy library and was trying to use it for this purpose. Below I am showing my functions.

f(x) = (p*x) dx

g(x) = alpha*(ln(f(x))) dx

I am trying to calculate the value of function g(x), but I could not find how to connect those two functions since they are composite functions.

import numpy as np
import math
from scipy.integrate import quad

def firstMethod(x, p1):
    return p1 * x

def firstIntegral():
    return quad(firstMethod, 0, 1, args=(4))[0]

def secondMethod(x, alpha):
    return alpha*math.log(firstIntegral)

def secondIntegral():
    return quad(secondMethod, 0, 10, args=(0.5))[0]

print(secondIntegral())

I am receiving the error of

TypeError: must be real number, not function

Looks like an error here: `math.log(firstIntegral)`. You can't take the logarithm of a function. You have to evaluate the function and then take the logarithm. — Nick ODell, Nov 09 '22 at 19:14

score 0 · Accepted Answer · answered Nov 09 '22 at 19:23

The problem is in secondMethod. Right now you're passing the function firstIntegral itself (functions are first class objects in Python). You need to call the function, i.e. put parentheses after its name and pass in any arguments it needs.

For example, you could change your secondMethod to this:

def secondMethod(x, alpha):
    return alpha * math.log(firstIntegral())  # Call the function.

It returns 3.4657359027997265.

how to integrate a composite function using scipy

1 Answers1