Discussion on IIT-JEE

In general, we know in math, for every operation, there will be some opposite operations as well. For example, for addition, subtraction is the opposite operation; for multiplication division is the opposite operation. In calculus, for differentiation, Integrals is the opposite operation. That is, “Integration is a process opposite to that of differentiation. In order to solve an integral, first of all we need to be familiar with all the basic formula’s in integrals. The few formula’s are given by:

1. [int] xndx = [x^[n+1]/ [n+1] ] + c.

2. [int 1/ x^ndx = 1/ [(1 **n) x ^[n ** 1]]] + c.

3. [int] exdx = ex + c.

4. [int] sin x dx = -cos x + c.

5. [int ] cos x dx = sin x + c.

6. [int 1/ x ] dx = lnx + c.

This formula list extents further which you can check in your text book. Beside knowing the formula, we need to know some of the methods of evaluating the integrals. The following are the methods of Integration which we need to be aware of to apply in solving the integrals. They are:

1. [int] (f(x) ± g(x)) dx = [int] f(x) dx ± [int ] g(x) dx + c.

2. [int [d/dx[f (x)] ]/ f(x)] dx = ln f(x) + c [substitution method].

by remembering these formula , it will be easy to solve all question