Double integral (dblquad) in SciPy - Mini Project: Build & Apply

Calculate Area Using Double Integral with dblquad

📖 Scenario: Imagine you want to find the area under a curved surface over a specific region. This is common in fields like physics and engineering when calculating volumes or probabilities.

🎯 Goal: You will learn how to use the dblquad function from scipy.integrate to calculate a double integral over a rectangular region.

📋 What You'll Learn

Create a function representing the surface to integrate

Define the limits of integration for both variables

Use dblquad to compute the double integral

Print the result of the integration

💡 Why This Matters

🌍 Real World

Double integrals are used in physics to find volumes under surfaces, in probability to find joint probabilities, and in engineering for stress analysis.

💼 Career

Knowing how to compute double integrals with tools like scipy is useful for data scientists and engineers working with continuous data and modeling.

1

Define the function to integrate

Create a function called f that takes two variables x and y and returns the value of x * y.

SciPy

# Define the function f(x, y) = x * y
# Your code here

Need a hint?

Remember, the function should take two inputs and return their product.

2

Set the integration limits

Create variables x_lower and x_upper with values 0 and 2 respectively. Also create two functions y_lower and y_upper that take x as input and return 0 and 3 respectively.

SciPy

def f(x, y):
    return x * y

# Define x_lower = 0 and x_upper = 2
# Define y_lower(x) = 0 and y_upper(x) = 3
# Your code here

Need a hint?

Use simple functions for y limits that ignore x and return constants.

3

Calculate the double integral using dblquad

Import dblquad from scipy.integrate. Then create a variable result that stores the output of dblquad called with f, x_lower, x_upper, y_lower, and y_upper.

SciPy

def f(x, y):
    return x * y

x_lower = 0
x_upper = 2
def y_lower(x):
    return 0
def y_upper(x):
    return 3

# Import dblquad and calculate the double integral
# Your code here

Need a hint?

Remember dblquad returns two values: the integral result and an estimate of the error.

4

Print the result of the double integral

Write a print statement to display the value stored in result.

SciPy

from scipy.integrate import dblquad

def f(x, y):
    return x * y

x_lower = 0
x_upper = 2
def y_lower(x):
    return 0
def y_upper(x):
    return 3

result, error = dblquad(f, x_lower, x_upper, y_lower, y_upper)

# Print the result
# Your code here

Need a hint?

The integral of x*y over x=0..2 and y=0..3 is 6.0