finding limits of integration during a change of variables

[Shinjo]

Hi. I have a problem with a question. Basically, I have an integral that goes from x=0 to x=1, and I'm supposed to make a change of variables like this:

Let x = 1 - y^2.

The problem I'm having is trying to find the limits of integration after the change of variables. Since y = +/- (x-1)^1/2, I have y = -1 or +1 for the lower limit. Am I supposed to just use either one? I'm so confused.

[arildno]

You need a bijection between the x's and the y's in this case.
That is, you should choose
EITHER y=\sqrt{1-x}
OR: y=-\sqrt{1-x}
Either one of them is okay; using both is wrong.