Probability Density Function Equation, Multivariable Calculus I have the following problem:
The formula for the normal distribution has a π in it. In this simplified version of the normal probability density function, solve for C. The correct answer has π in it. 
$$
1 = C\int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+y^2)}dydx
$$
Can anybody tell me how to solve this problem? Any help is appreciated!

You could do all of the integration, as the comments have pointed out. However, it is possible that you have been given as a fact, or proven in class that 
$$\int_{-\infty}^\infty e^{-t^2}\,dt = \sqrt\pi.$$ Thus, use this fact twice:
\begin{align*}
\int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+y^2)}\,dydx
&= \int_{-\infty}^\infty e^{-x^2}\left[\int_{-\infty}^\infty e^{-y^2}\,dy\right]dx\\
&=\sqrt\pi\int_{-\infty}^\infty e^{-x^2}\,dx\\
&=\sqrt\pi\cdot\sqrt\pi\\
&= \pi.
\end{align*}
This implies that $C = 1/\pi$.
Of course, this answer is invalid, if you are not allowed to use that fact.
