Finding $\int_{-\infty}^{\infty}e^{x^2}\,dx$

Question

I was wondering if $\int_{-\infty}^{\infty}e^{x^2}\,dx$ is defined, I think it isn't. But I dunno how to start proving/disproving.

Answer 1

Well, notice that $e^{x^2}\geq 1$ for all $x$ so that $$ \int_{-\infty}^\infty e^{x^2}\;dx \geq \int_{-\infty}^\infty 1 \; dx $$