Simpson's rule (simpson) in SciPy - Mini Project: Build & Apply

Calculate Area Under Curve Using Simpson's Rule

📖 Scenario: Imagine you are a scientist measuring the speed of a car at different times. You want to find out how far the car traveled during that time by calculating the area under the speed-time graph.

🎯 Goal: You will use Simpson's rule to calculate the approximate area under the curve from given speed measurements at specific times.

📋 What You'll Learn

Create a list called time_points with exact values: 0, 1, 2, 3, 4

Create a list called speed_measurements with exact values: 0, 10, 20, 10, 0

Create a variable called dx and set it to 1

Use scipy.integrate.simpson to calculate the area under the curve using speed_measurements and dx

Print the calculated area with the exact variable name area

💡 Why This Matters

🌍 Real World

Simpson's rule helps scientists and engineers estimate areas under curves when exact formulas are hard to find, such as calculating distance from speed data.

💼 Career

Understanding numerical integration like Simpson's rule is useful in data analysis, physics, engineering, and any job involving measurement and estimation from data.

1

Create time and speed data lists

Create a list called time_points with values 0, 1, 2, 3, 4 and a list called speed_measurements with values 0, 10, 20, 10, 0.

SciPy

# Create the lists time_points and speed_measurements
# Your code here

Need a hint?

Use square brackets to create lists with the exact numbers given.

2

Set the spacing variable dx

Create a variable called dx and set it to 1 to represent the equal spacing between time points.

SciPy

time_points = [0, 1, 2, 3, 4]
speed_measurements = [0, 10, 20, 10, 0]
# Create the variable dx and set it to 1
# Your code here

Need a hint?

Just assign the number 1 to the variable dx.

3

Calculate area using Simpson's rule

Import simpson from scipy.integrate and use it to calculate the area under the curve by passing speed_measurements and dx. Store the result in a variable called area.

SciPy

time_points = [0, 1, 2, 3, 4]
speed_measurements = [0, 10, 20, 10, 0]
dx = 1
# Import simpson and calculate area using simpson(speed_measurements, dx=dx)
# Store the result in area
# Your code here

Need a hint?

Use from scipy.integrate import simpson and then call simpson(speed_measurements, dx=dx).

4

Print the calculated area

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

SciPy

from scipy.integrate import simpson

time_points = [0, 1, 2, 3, 4]
speed_measurements = [0, 10, 20, 10, 0]
dx = 1

area = simpson(speed_measurements, dx=dx)
# Print the area
# Your code here

Need a hint?

Use print(area) to show the result.