The process of determining an integral of a given function is defined as integration of a function.

**Indefinite Integrals**

**Concept of Indefinite Integral**

In differential calculus, we have learned how to calculate the
differential coefficient *f *′* *(*x*)* *of a given function* f *(*x*)* *with
respect to* x*.* *In this chapter, we have to find out the* *primitive
function *f* (*x*) (i.e. original function) whenever its derived
function *f* ′
(*x*) (i.e. derivative of a function) is given, such process is called
integration or anti differentiation.

∴ Integration is the
reverse process of differentiation

We know that *d/dx* (sin *x* ) = cos *x*. Here cos *x*
is known as **Derived function**, and sin *x *is known as **Primitive function** [also called as Anti
derivative function (or) Integral function].

**Definition 2.1**

A function *F* (*x*) is said to be a primitive
function of the derived function *f* (*x*) , if *d/dx *[* F *(*x*)]=* f *(*x*)

Now, consider the following examples which are already known to
us.

From the above examples, we observe that 3*x*^{2} is
the derived function of the primitive functions *x*^{3} , *x*^{3}
+ 5 , *x*^{3}
– 3/2 , *x* ^{3}
+ *e* , *x*^{3}
− *π* , ... and
which indicates that the primitive functions are need not be unique, even
though the derived function is unique. So we come to a conclusion that *x*
^{3} + *c* is the
primitive function of the derived function 3*x*^{2} .

∴ For every derived
function, there are infinitely many primitives by choosing *c* arbitrarily
from the set of real numbers **R**. So we called these integrals as
indefinite integrals.

**Definition 2.2**

The process of determining an integral of a given function is
defined as integration of a function.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

12th Business Maths and Statistics : Chapter 2 : Integral Calculus - I : Concept of Indefinite Integral |

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