square both sides ? Woahhh


Hi,

When integrating (indefinite) e^(sqrtx)dx, we simplify by substituting
u=sqrtx

Then we do the unthinkable, square both sides of this subistition
equation, u^2 = x

From there on it's just a matter of finding out what dx is and
replacing x and dx in the original integral and going on about our
business, then substituting the answer back into x's.

My question is, when doing this trick, why is squaring both sides not
as dangerous as before. In no textbook or online tutorial did it tell
me to check the answer by differentiating, or even noted this possibly
dangerous step.

Are equations of the form a = sqrt(b) safe for "Squaring both sides"
or is there another reason for the lack of warning in this step? Maybe
a reason that deals with integration?


D. Bahar

.

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