What are the two main types of integration?

The two main types of integration are definite and indefinite integration.

Definite integration involves calculating the accumulation of quantities, which gives a numerical result representing the area under the curve of a function between two specified limits. This type of integration is fundamental in applications such as finding the total distance traveled over a certain time period when given a velocity function.

Indefinite integration, on the other hand, represents the general form of antiderivatives of a function. It results in a family of functions and is expressed with a constant of integration, indicating that there are infinitely many antiderivatives for a given function. This aspect of integration is crucial for solving differential equations and understanding the relationship between functions and their rates of change.

In summary, distinguishing between these two types allows for a deeper understanding of integration in calculus and its applications across various fields.