Answer:
Converges to [tex]\frac{\sqrt{\pi }}{2}[/tex]
Step-by-step explanation:
[tex]\int _0^{\infty \:}e^{-x^2}dx[/tex] = [tex]\lim_{b \to \infty}[/tex] [tex]\int _0^{b \:}e^{-x^2}dx[/tex] = [tex]\frac{\sqrt{\pi }}{2}[/tex]
steps:
write improper integral as a limit
solve integral
apply limit
If limit exists and this number is finite, the improper integral converges
