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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Wednesday, January 25, 2006

### Better Choices

A new way of anti - differentiating was taught today. Not all products can be integrated by reversing the Chain rule. Sometimes, using Substitution will make it look even worse than what we could've imagined. So with the complexity of some equations, the method of INTEGRATION BY PARTS is introduced.

The rule of integration by parts can be written as:
$\int f(x) g'(x)\,dx = f(x) g(x) - \int g(x) f'(x)\,dx$

According to the rule, the integral of a product of two functions may be written as a difference, one term of which is a new integral. In most cases, the new integral is simpler than the original integral. Therefore, this technique requires the importance of designating the factors f(x) and g'(x) of the original integrand in such way that f(x) simplifies under differentiation while the factor g'(x) does not become more complicated under the integration.

As what I've just mentioned, assigning the factors is a crucial aspect in performing this technique. To get better chances of heading to the correct answers, L I A T E must be taken into consideration.

L I A T E as in

L - orgarithmic
I - nverse Trig
A - lgebraic
T - rigonometric
E - xponential

It is also significant to know which method applies to a particular equation. In this way, it saves up time and makes it a lot easier.

So make better choices and always remember the past lessons and techniques that were recently learned... then your off to university... I think... well not really... but it's a good start though... *smiles*