How to Compute the Area Between Two Curves in Python?

To compute the area between two curves in Python, you can use numerical integration techniques, such as the trapezoidal rule or the Simpson’s rule, available in libraries like SciPy. Here’s an example using the trapezoidal rule:

import numpy as np
from scipy.integrate import trapz

# Define the x-values and two curves as functions of x
x = np.linspace(0, 10, 100)
curve1 = x ** 2
curve2 = 2 * x

# Calculate the y-values for the area between the curves
area_y = np.abs(curve1 - curve2)

# Compute the area between the curves using the trapezoidal rule
area = trapz(area_y, x)

print("Area between the curves:", area)

In this example, we first define the x-values using np.linspace() to create an array of 100 evenly spaced values between 0 and 10. Then, we define two curves (curve1 and curve2) as functions of x. You can modify these curves based on your specific requirements.

Next, we calculate the y-values for the area between the curves by taking the absolute difference between curve1 and curve2 using np.abs(). This creates a new array (area_y) that represents the vertical distance between the curves at each x-value.

Finally, we use the trapz() function from SciPy to compute the area between the curves by performing numerical integration using the trapezoidal rule. The trapz() function takes the y-values (area_y) and the corresponding x-values (x) as inputs.

After computing the area, it is printed as the output.

Remember to have SciPy installed (pip install scipy) before running this code. You can explore other numerical integration methods available in SciPy, such as Simpson’s rule (scipy.integrate.simps()), depending on your specific needs.