Re: Positive/Negative after taking the square root
- From: matt271829-news@xxxxxxxxxxx
- Date: Wed, 28 Nov 2007 16:21:59 -0800 (PST)
On Nov 29, 12:06 am, matt271829-n...@xxxxxxxxxxx wrote:
<snip>
When you substitute u = x^2 you're losing information about which of
the two possible values of x you're dealing with. (This always happens
when the inverse function is multi-valued.)
A simple example of this, which I suppose is vaguely related to the
matter in hand, would be a definite integral between x = -1 and x = 1.
With the substitution u = x^2 this appears to become an integral
between u = (-1)^2 = 1 and u = 1^2 = 1, which is obviously wrong.
.
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