Why numerical integration computes areas in SciPy - See It in Action

Why Numerical Integration Computes Areas

📖 Scenario: Imagine you want to find the area under a curve that shows how fast a car is moving over time. This area tells you how far the car traveled. We will use numerical integration to find this area.

🎯 Goal: You will create a simple list of speed values, set up a time step, use numerical integration to calculate the total distance traveled, and then print the result.

📋 What You'll Learn

Create a list called speeds with the values: 0, 10, 20, 30, 40, 50

Create a variable called time_step and set it to 1

Use scipy.integrate.simps to calculate the area under the speed curve and store it in distance

Print the value of distance

💡 Why This Matters

🌍 Real World

Numerical integration helps us find distances, areas, and totals when we only have data points, like measuring how far a car traveled from speed readings.

💼 Career

Data scientists use numerical integration to analyze real-world data where exact formulas are unknown, such as in physics, engineering, and finance.

1

Create the speed data

Create a list called speeds with these exact values: 0, 10, 20, 30, 40, 50.

SciPy

# Create the list speeds with the given values
# Your code here

Need a hint?

Use square brackets to create a list and separate numbers with commas.

2

Set the time step

Create a variable called time_step and set it to 1 to represent the time between speed measurements.

SciPy

speeds = [0, 10, 20, 30, 40, 50]
# Create the variable time_step and set it to 1
# Your code here

Need a hint?

This is just a number that tells us how far apart the speed readings are in time.

3

Calculate the distance using numerical integration

Import simps from scipy.integrate. Use simps with speeds and dx=time_step to calculate the area under the speed curve. Store the result in a variable called distance.

SciPy

speeds = [0, 10, 20, 30, 40, 50]
time_step = 1
# Import simps and calculate distance using simps with speeds and dx=time_step
# Your code here

Need a hint?

Use from scipy.integrate import simps to import the function. Then call simps(speeds, dx=time_step).

4

Print the total distance

Write a print statement to display the value of distance.

SciPy

from scipy.integrate import simps

speeds = [0, 10, 20, 30, 40, 50]
time_step = 1

distance = simps(speeds, dx=time_step)
# Print the distance
# Your code here

Need a hint?

Use print(distance) to show the result.