# Math Help - Use comparison test to determine whether interval converges.

1. ## Use comparison test to determine whether interval converges.

Integral of 2^(-x^2) from 1 to infinity.

2. for x > 1

$x\cdot 2^{-x^{2}} > 2^{-x^{2}}$

3. Originally Posted by TKHunny
for x > 1

$x\cdot 2^{-x^{2}} > 2^{-x^{2}}$
How did you derive this?

4. Well, "derive" is not that great a word for the process. I wanted to invent a structure that was easily integrated. The $x^{2}$ in the exponent suggested another 'x' out front would be good - thinking about the simple substitution $u = x^{2}$. After that, it was just a bit of thought to determine EXACTLY why the problem suggested the Domain $[1,\infty)$ rather than $[0,\infty)$.

That's about it. You just have to think it through and figure it out.