1. **Problem statement:** Find the normalizing constant $c$ such that $$\int_{-\infty}^\infty c e^{-x^2/2} \, dx = 1.$$ 2. **Formula and important rules:** The integral $$\int_{-\infty}^\infty e^{-x^2/2} \, dx = \sqrt{2\pi}$$ is a well-known Gaussian integral. To normalize the function $c e^{-x^2/2}$ so that its integral over the entire real line equals 1, we need to find $c$ such that $$c \int_{-\infty}^\infty e^{-x^2/2} \, dx = 1.$$ 3. **Intermediate work:** Substitute the known integral value: $$c \sqrt{2\pi} = 1.$$ 4. **Solve for $c$:** $$c = \frac{1}{\sqrt{2\pi}}.$$ 5. **Explanation:** The constant $c$ scales the function $e^{-x^2/2}$ so that the total area under the curve is 1, making it a valid probability density function for the standard normal distribution. **Final answer:** $$c = \frac{1}{\sqrt{2\pi}}.$$