# Finding limits of integration during a change of variables

1. Mar 16, 2005

### 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.

2. Mar 16, 2005

### 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.