calculus - Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \dfrac{\sqrt \p
How to prove $$\int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}$$ ... I know this: Define $f$ and $g$ as: $$f(x):=\left(\int_0^x e^{-t^2}dt\right)^{2} \ \ \ \text{and} \ \ \...