Numerical integration

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/numerical-integration

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the error estimation?Crucial for determining the accuracy of approximations and controlling computational effort
2. What is the computational significance?Enables solutions for complex problems in science, engineering, finance, and computer graphics
3. Why do we need numerical integration when we can't find exact answers?Some real‑world functions don't have a simple formula that gives their area. Numerical integration lets us get a close answer by adding up many small pieces, so we can still learn about the function.
4. How do the Trapezoidal Rule and Simpson's Rule help us find areas?The Trapezoidal Rule uses straight‑line pieces to connect points on the curve, while Simpson's Rule uses curved (parabolic) pieces that fit the curve better. Both add up the pieces to estimate the total area.

Integrand: The function that is being integrated in a definite integral expression.
Antiderivative: A function whose derivative is the original function; used in analytical integration.
Quadrature: A synonym for numerical integration, referring to the process of finding an approximate area under a curve.