Integral

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/integral

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 mathematical framework?Integral calculus, a core branch of mathematical analysis
2. What is the fundamental theorem of calculus?Establishes the inverse relationship between differentiation and integration
3. How does integration help us find area under a curve?A definite integral gives the area that lies below a curve and above the x‑axis between two points. It can also give other things like volume or work.
4. Who were the first people to think about integration?The idea of integration started with ancient Greek mathematicians such as Eudoxus and Archimedes. They used the method of exhaustion, drawing many-sided polygons to get closer and closer to the true area.

Antiderivative: A function whose derivative is the original function.
Riemann Sum: An approximation of an integral by summing the areas of rectangles.
Probability Density Function (PDF): A function describing the likelihood of a continuous random variable taking on a given value.