The concept of an anti-derivative, also known as an indefinite integral, is closely related to the concept of integration. In calculus, integration is a mathematical process that is used to find the area under a curve or to determine the accumulation of a quantity over time.
An anti-derivative is a function that, when differentiated, will produce a given function. In other words, it is the inverse operation of differentiation. The process of finding an anti-derivative is often called integration.
The fundamental theorem of calculus states that integration and differentiation are inverse operations. This means that if a function is differentiated, the resulting derivative can be integrated to produce the original function. Similarly, if a function is integrated, the resulting indefinite integral can be differentiated to produce the original function.
This relationship between integration and differentiation is why the terms "anti-derivative" and "integration" are often used interchangeably. In general, integration is the process of finding an anti-derivative, and an anti-derivative is a function that can be obtained through integration