Triple integral (tplquad) in SciPy - Mini Project: Build & Apply

Calculate Volume Using Triple Integral with tplquad

📖 Scenario: Imagine you are a scientist studying a 3D shape defined by a mathematical function. You want to find the volume under this shape within certain limits.

🎯 Goal: You will calculate the volume under the function f(x, y, z) = x + y + z over a specific 3D region using the tplquad function from scipy.integrate.

📋 What You'll Learn

Create a function f that takes three variables x, y, and z and returns x + y + z.

Set the integration limits for x from 0 to 1.

Set the integration limits for y from 0 to 2.

Set the integration limits for z from 0 to 3.

Use tplquad to calculate the triple integral of f over these limits.

Print the calculated volume.

💡 Why This Matters

🌍 Real World

Triple integrals are used in physics and engineering to calculate volumes, masses, and other quantities in three-dimensional spaces.

💼 Career

Understanding how to compute triple integrals helps in fields like data science, physics simulations, and engineering design where 3D data and volumes are analyzed.

1

Define the function to integrate

Create a function called f that takes three arguments x, y, and z and returns the sum x + y + z.

SciPy

# Define the function f(x, y, z) that returns x + y + z
# Your code here

Need a hint?

Remember to define a function using def and return the sum of the three inputs.

2

Set the integration limits

Create three variables: x_lower set to 0, x_upper set to 1, y_lower set to 0, y_upper set to 2, z_lower set to 0, and z_upper set to 3.

SciPy

def f(x, y, z):
    return x + y + z

# Set integration limits for x, y, and z
# Your code here

Need a hint?

Assign the exact numbers to the variables as given.

3

Calculate the triple integral using tplquad

Import tplquad from scipy.integrate. Then use tplquad to calculate the triple integral of f over x from x_lower to x_upper, y from y_lower to y_upper, and z from z_lower to z_upper. Store the result in a variable called volume.

SciPy

def f(x, y, z):
    return x + y + z

x_lower = 0
x_upper = 1
y_lower = 0
y_upper = 2
z_lower = 0
z_upper = 3

# Import tplquad and calculate the triple integral
# Your code here

Need a hint?

Remember the order of integration in tplquad is func, x_lower, x_upper, y_lower_func, y_upper_func, z_lower_func, z_upper_func. Use lambda functions for the y and z limits.

4

Print the calculated volume

Write a print statement to display the value of the variable volume.

SciPy

from scipy.integrate import tplquad

def f(x, y, z):
    return x + y + z

x_lower = 0
x_upper = 1
y_lower = 0
y_upper = 2
z_lower = 0
z_upper = 3

volume, error = tplquad(f, x_lower, x_upper, lambda x: y_lower, lambda x: y_upper, lambda x, y: z_lower, lambda x, y: z_upper)

# Print the volume
# Your code here

Need a hint?

Use print(volume) to show the result.