Understanding IITJEE Integration: The Easy Way - 1

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Suppose you were told that a function had a gradient given by
Could you work out that function?

By referring back to differentiation, you would notice that this gradient was given by the function

Is this then our function?

Not necessarily! We would get the same gradient for the function

This process of finding the function from it's gradient, is called Integration.

This is only the most basic use of integration. Together with differentiation, it is probably the most important area of maths.

The basic method of integration, is to reverse differentiation.

To differentiate, we multiplied by the power, then subtracted 1 from the power

To integrate, we reverse this exactly.

First add 1 to the power, then divide by the new power.

Notice that there is a constant added onto the function. This is because, as in the case above, we do not know whether or not a number must be added to our function.

Example

Find the curve whose gradient is
Add 1 the power an divide by new power.
Simplify		Important If you leave off the c, your answer is wrong and you will lose a mark