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Integration By Substitution

An explanation of how integration by substitution works:

Integration by substitution.

Integration By Parts

Some time ago, a student of mine introduced me to a novel way of doing Integration by Parts (IBP). It's called the "Tabular Method". It makes the whole process much simpler, and using the tabular method, IBP can be used to do many more things other than pure integration!

I've done a bit of research into the topic, and I've written some documents that I hope might help you learn about IBP, and the tabular method in particular.

The first is aimed at A2-level students, to show you how the tabular method works:

DIS is how you do it!

The second is primarily aimed at teachers and Exam Boards, to show what a wonderful tool the tabular method of IBP can be:

More on the Tabular Method of IBP

This one shows you how you can use parts, rather than trig identities, to integrate even powers of sine and cosine:

Even Powers of Sine and Cosine

Since Integration by Parts is the Product Rule for Integration, have you ever wondered if there was a Quotient Rule for Integration?

Quotient Rule for Integration

How to do Integration

I've written a couple of documents that I'm hoping will help tackle A2-Level integration questions in general. The first is a general outline of the process by which you determine what tool to use to do the integration. Included is a decision tree to help you find the right tool to use.

How To Do Integration I: The Process

The second document contains complete worked solutions to all integration questions in Edexcel C4 exams from June 2005 to June 2014 inclusive. The solutions include the very important HOW I arrived at the solution.

How To Do Integration II: The Questions

Numerical Integration

When you can't integrate a function algebraically, you might have to resort to doing it numerically.

Here's one idea. It's called the Trapezium Rule:

The Trapezium Rule

And here's another. This one is called Simpson's Rule:

Simpson's Rule


Here you can find out the easist possible way of doing Integration by Parts quickly and accurately!!