Q&A #4268


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From: Pat Ballew (for Teacher2Teacher Service)
Date: Jul 07, 2000 at 16:43:09
Subject: Re: integration

I guess all integration is an art in some sense.
Once you get beyond the easy ones, everything is a matter of substitution
in some form or another.  I guess I think of integration by parts as a
substitution approach because it requires us to pick functions to represent
u, and dv, etc.

The best advice I can give you is to study lots of examples, and develop an
arsenal of approaches, then, "if it looks like a duck" try what you would try
for ducks.

I'm sorry if that seems like not much help, but sometimes integration
reminds me of geometry proofs, you stare at a proof and try lots of stuff and
seem to get nowhere, then someone says "draw this line" and all is clear.
Sometimes with integrals, its easy if you see what substitution to make, but
seeing the right substitution is that "magic" part of genius that Marc Kac
spoke of.

good luck

 -Pat Ballew, for the Teacher2Teacher service

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