integrate e^(-x^2) from zero to infinity?

Consider the double integral I² = ∫∫ e^{-(x^2 + y^2)} dydx ...convert to polar coordinates

Thanks. What limit should I use for polar coordinate?

between π and 0

What level are you working at here? You've been asking a lot of questions, some of which seem to be sort of A2 Maths level and some of which wouldn't appear until degree level; and I can't help but notice that when people mention a method you're not often familiar with the method, let alone the problem itself... maybe I'm reading too much into it (but if you let us know what level you're at we can probably help more).

And to evaluate -x^p *e^(-x) from zero to infinity where p is constant

between π and 0

Are you sure you mean that?

There are 2 normal ways of doing this:

Find $\int_0^\infty \int_0^\infty e^{-x^2-y^2} \, dy \, dx$

which gives a range for theta of 0 to pi/2, or

find $\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-x^2-y^2} \, dy \, dx$

which gives a range for theta of 0 to 2pi.

She hasn't posted working, but I would suspect this is why the OP is off by a factor of 2.

ohhhh so limit is 0 to pi/2 ? Why? 0 to pi does seem to make sense as we want half of -infinity to infinity?

paranomase: you don't need the error function to do the indefinite integral from -infinity to infinity.

Um, the integral from -infinity to infinity is a *definite* integral, not an indefinite one.

getting improper mixed up with indefinite