Trapezoidal rule (trapezoid) in SciPy - Mini Project: Build & Apply

Calculate Area Under Curve Using Trapezoidal Rule

📖 Scenario: You have collected data points representing the speed of a car at different times during a trip. You want to estimate the total distance traveled by calculating the area under the speed-time curve.

🎯 Goal: Use the trapezoidal rule to calculate the approximate area under the curve from the given speed and time data points.

📋 What You'll Learn

Create two lists named time and speed with exact values

Create a variable named dx to represent the spacing between time points

Use scipy.integrate.trapezoid with speed and dx to calculate the area

Print the calculated area using print(area)

💡 Why This Matters

🌍 Real World

Estimating distance traveled from speed data is common in vehicle tracking and sports analytics.

💼 Career

Data scientists often use numerical integration methods like the trapezoidal rule to analyze sensor data and calculate totals from sampled measurements.

1

Create the time and speed data lists

Create a list called time with values [0, 1, 2, 3, 4] representing time in seconds. Create another list called speed with values [0, 10, 20, 15, 10] representing speed in meters per second.

SciPy

# Create the time and speed lists
# Your code here

Need a hint?

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

2

Set the spacing between time points

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

SciPy

time = [0, 1, 2, 3, 4]
speed = [0, 10, 20, 15, 10]
# Create dx variable with value 1
# Your code here

Need a hint?

Set dx to the difference between consecutive time points, which is 1 second.

3

Calculate the area using trapezoidal rule

Import trapezoid from scipy.integrate. Use trapezoid(speed, dx=dx) to calculate the area under the speed curve and store it in a variable called area.

SciPy

time = [0, 1, 2, 3, 4]
speed = [0, 10, 20, 15, 10]
dx = 1
# Import trapezoid and calculate area
# Your code here

Need a hint?

Use from scipy.integrate import trapezoid to import the function.

4

Print the calculated area

Print the value of the variable area using print(area).

SciPy

from scipy.integrate import trapezoid

time = [0, 1, 2, 3, 4]
speed = [0, 10, 20, 15, 10]
dx = 1
area = trapezoid(speed, dx=dx)
# Print the area
# Your code here

Need a hint?

Use print(area) to show the result.