Revision:Integration by Substitution

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Integration by Substitution

It is possible to transform a difficult integral to an easier integral in a different variable using a substitution. By using substitutions, we can show that:

where and g(u) is much easier to integrate than f(x). Here, and so

Worked Examples

Find Here, we have a rather nasty term inside the bracket, so we let .

We can now find by simple differentiation. By rearrangement, Making the u-substitution and the dx-substitution in the original problem, we transform it to

And since ,

Using a Substitution

Sometimes you will be told to integrate a function by using a substitution. For example, in the above first example, you might be told without being having to make it up yourself.

Comments

Diagrams are missing here. Alternatively, the necessary maths could be written in LaTeX.