CS(0) Brief Introduction to Integrals

And Intro to Computational Statistics

In the following articles, we will learn some basic concepts about computational statistics. Computational Statistics is a field that combines statistical theory with computational methods to analyze and interpret data. It focuses on developing algorithms to perform statistical analysis, especially when dealing with large datasets or complex models that are computationally intensive.

But before we continue, we need to review some concepts about calculus. We have already learned about differentiation here and here, and in this post, we will learn about integral calculus.

What are Integrals?

At their core, integrals are a mathematical way to represent the accumulation of quantities. You can think of them as a method for summing up tiny parts to get the whole. In calculus, integrals are often used to find areas under the curves, but they can also represent other accumulated quantities like distance traveled volume, or probability.

Key idea: The Area Under the Curve
Imagine you have a curve on a graph, like the function f(x) = x², and you want to find the area between this curve and the x-axis over a certain interval, let’s say x=1 and x=3. This area is f(x) integral from 1 to 3. The notion for this is: