Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 80

Answer

It is not appropriate to substitute $u=x^2,\quad x=\sqrt{u},\quad dx=du/(2/\sqrt{u})$.

Work Step by Step

This is not appropriate because if we take $u=x^2$ then $x=\pm\sqrt{u}$. Only for nonnegative $x$ we could write $x=\sqrt{u}$ and this substitution would work only if the region of integration he nonnegative part of the real line. Since within the given bounds, $-1$ and $1$, $x$ takes both positive and negative values, this substitution won't work.
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