Numerical integration (integral, trapz) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the integral function in MATLAB do?

The integral function calculates the numerical integral (area under the curve) of a function over a specified interval using adaptive quadrature methods.

beginner

How does the trapz function approximate an integral?

trapz uses the trapezoidal rule, which approximates the area under a curve by dividing it into trapezoids and summing their areas.

beginner

Syntax of integral function in MATLAB?

Basic syntax: q = integral(fun, a, b) where fun is the function handle, and a, b are the integration limits.

intermediate

When should you prefer trapz over integral?

Use trapz when you have discrete data points and want to approximate the integral, especially if the function is not easily expressed as a function handle.

intermediate

What is the main difference between integral and trapz in MATLAB?

integral works with function handles and uses adaptive methods for higher accuracy, while trapz works with vectors of data points and uses the trapezoidal rule.

Which MATLAB function uses adaptive quadrature to compute integrals?

A diff

B integral

C sum

D trapz

integral uses adaptive quadrature, while trapz uses the trapezoidal rule.

What input does trapz require to approximate an integral?

A Matrix multiplication

B Function handle

C Symbolic expression

D Discrete data points

trapz approximates integrals from discrete data points.

What does the trapezoidal rule approximate the area under a curve with?

A Trapezoids

B Circles

C Rectangles

D Triangles

The trapezoidal rule approximates the area using trapezoids.

Which function is better for integrating a smooth function defined by a formula?

A plot

B trapz

C integral

D diff

integral is better for smooth functions defined by formulas.

What is the correct syntax to integrate function f from 0 to 1 using integral?

A integral(f, 0, 1)

B trapz(f, 0, 1)

C integral(0, 1, f)

D trapz(0, 1, f)

The syntax is integral(f, 0, 1) where f is a function handle.

Explain how the integral and trapz functions differ in MATLAB and when to use each.

Think about the input types and accuracy methods.

Describe the trapezoidal rule and how trapz applies it to approximate integrals.

Imagine connecting points with straight lines and calculating the area.