Which functions can be integrated

Integrability of a function (level sec. I)

Integration of functions is required in all science subjects. This is because the main task of integral calculus is to calculate an area (the area below a function graph). In the context of school mathematics, a function can be integrated if the function is continuous (in the interval to be integrated).

Integrability of a function

This chapter only deals with the determination of the integrability of a function (not with the integration regulations).

According to the mathematical definition, a function can be integrated in an interval [a, b] if the function is “restricted” (i.e. the limit values ​​of the upper and lower sums exist and are equal, i.e. there is no so-called pole). This “limitation” is a prerequisite for the integrability of a function. If the function is now continuous in the entire integration interval [a, b], then the “definite integral” exists (=> a unique value)

Prerequisite for integrability

The prerequisite that a function can be integrated is that the function is continuous

Note:
Every function that is continuous can also be integrated. A function that can be integrated is not automatically continuous in all places (e.g. the Signum function - integrable but continuous in all places).