Numerical integration (integral, trapz) in MATLAB - Mini Project: Build & Apply

Numerical integration using integral and trapz in MATLAB

📖 Scenario: You are working as a data analyst and need to calculate the area under a curve representing a physical measurement over time. This is a common task in science and engineering to find total quantities from rate data.

🎯 Goal: Build a MATLAB script that calculates the integral of a function using both the integral function and the trapz function for numerical integration. You will compare the results to understand how these methods work.

📋 What You'll Learn

Create a vector of x values from 0 to 10 with 100 points

Create a vector y with the function values y = sin(x)

Use the integral function to calculate the integral of sin(x) from 0 to 10

Use the trapz function to calculate the integral approximation from the x and y vectors

Print both results to compare

💡 Why This Matters

🌍 Real World

Numerical integration is used in physics, engineering, and data analysis to find total quantities like distance from speed or area under curves from measurements.

💼 Career

Understanding numerical integration helps in roles like data analyst, engineer, or scientist where you work with experimental data or simulations.

1

Create the x vector

Create a vector called x with 100 points linearly spaced from 0 to 10 using the linspace function.

MATLAB

% Create the x vector with 100 points from 0 to 10
% Your code here

Need a hint?

Use linspace(0, 10, 100) to create 100 points between 0 and 10.

2

Calculate y = sin(x)

Create a vector called y that contains the sine of each value in x using the sin function.

MATLAB

x = linspace(0, 10, 100);
% Calculate y as sin(x)
% Your code here

Need a hint?

Use y = sin(x); to get sine values for each x.

3

Calculate integrals using integral and trapz

Calculate the integral of sin(x) from 0 to 10 using the integral function and store it in int_val. Then calculate the integral approximation using trapz with x and y and store it in trapz_val.

MATLAB

x = linspace(0, 10, 100);
y = sin(x);
% Calculate int_val using integral
% Calculate trapz_val using trapz
% Your code here

Need a hint?

Use integral(@sin, 0, 10) and trapz(x, y) to calculate integrals.

4

Display the results

Print the values of int_val and trapz_val using fprintf to show the integral results with 6 decimal places.

MATLAB

x = linspace(0, 10, 100);
y = sin(x);
int_val = integral(@sin, 0, 10);
trapz_val = trapz(x, y);
% Print int_val and trapz_val
% Your code here

Need a hint?

Use fprintf('Integral using integral: %.6f\n', int_val); and similarly for trapz_val.