특이적분 $\displaystyle \int _ {0} ^ {\infty} e^ {-2 x^ {2}} d x$ 의 값은?

• ①$\displaystyle \frac{\sqrt{\pi}} {\sqrt{2}}$
• ②$\displaystyle \frac{\sqrt{\pi}} {2}$
• ③$\displaystyle \frac{\sqrt{\pi}} {2 \sqrt{2}}$
• ④$\displaystyle \frac{\sqrt{\pi}} {4}$
• ⑤$\displaystyle \frac{\sqrt{\pi}} {4 \sqrt{2}}$