CALCULUS Understanding Its Concepts and Methods

Change of variable, Substitution

If
*u* = *g*(*x*)
is a differentiable function of
*x*,
then
*du = g'*(*x*)* dx*.
This can be used to rewrite an integral involving
*x *and
*dx*
as one involving
*u *and
*d**u*.
The point of making a change of variable is to rewrite an integral in a
simpler form that can be integrated by standard means.

Change of variable for an indefinite integral

Change of variable for a definite integral

Change of variable is also referred to as substitution.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.