What is a definite integral?

A definite integral is a numerical value that expresses the area under the graph of a function over a given interval. Formally, if a function f(x) is given, the definite integral from a to b is written as:

[ \int_a^b f(x) , dx ]

It calculates the accumulated value of the function from point a to point b. For example, if f(x) is the velocity of movement, then the integral will give the distance traveled.

The definite integral can be represented as the limit of the sum of the areas of rectangles under the curve with an infinite subdivision of the interval [a, b]. This is a fundamental tool in mathematical analysis and is used to calculate areas, volumes, work, and other physical quantities.