Question

What does integration mean?

Answer 1

We can say that integration is a process like any other stepwise processes in mathematics. But there are various approaches where it is used. We also call it an antiderivative process. Let’s check the scenarios one by one.

Complete step by step solution:
I.Integration is used in mathematics as well as in engineering processes.
II.In mathematics we call it an “antiderivative “process. That is integration and derivatives are exactly opposite processes of each other. For example,
Derivative of ${x^2}$ is 2x and the integration of 2x is ${x^2}$.
III.We perform the integration of a differential equation where a symbol like curved letter S is used and is written as $\int {}$is used.
$\int {2x} dx = {x^2} + C$
Where C is the constant of integration.
IV.Sometimes the integration has limits or we can say bindings that are upper and lower limits.
$\int\limits_a^b {f\left( x \right)} dx$ and is called definite integral and the other with no bounds is called indefinite integral.
V.Integration is used to find area, volume of the given function also.
VI.There are certain rules that are also followed when we integrate the functions.
VII.Functions that are integrated are logarithmic, algebraic, exponential and trigonometric.
VIII.Overall it is a full whole chapter in mathematics with different rules and methods mentioned to solve particular types of integration.
As we mentioned the word rules above are integration by parts and sometimes substitution.

Note: Note that some functions are integrated such that they have fixed answers in mathematics and those are used directly in competitive exams. Like trigonometric functions, inverse trigonometric functions have précised answers already noted.
This word integration is sometimes used as data integration, digital integration but that is not the mathematical integration rather that might mean collaboration or making it more précised. Whereas electronics uses the word integrated circuit and designs.