### Primitive Or Anti derivative

A functionÂ is called a primitive of a function f(x) ifÂ

For example,Â is primitive ofÂ beacauseÂ

### Indefinite Integrals

If f(x) is any anti-derivative or primitive of a function f(x) then the most general anti-derivative of f(x) is called an indefinite integral.

Let f(x) be a function. Then the collection of all its primitives is called the indefinite integral of f(x) and is denoted byÂ Â Thus,

whereÂ is primitive of f(x) and C is an arbitrary constant known as the constant of integration.

HereÂ is integral sign , f(x) is the integrated , x is the variable of integration and d x is the element of integration of differential of x.

The process of finding an indefinite integral of a given function is called integration of the function.

It follows from the above discussion that integrating a function f(x) means finding a functionÂ such thatÂ