Integral from $0$ to Infinity of $e^{-3x^2}$? How do you calculate the integral from $0$ to Infinity of $e^{-3x^2}$? I am supposed to use a double integral. Can someone please explain? Thanks in advance.

There is a neat trick. Set $$I = \int_{0}^\infty e^{-3x^2}dx.$$
Then 
$$
I^2 = \left(\int_0^\infty e^{-3x^2} dx\right) \left(\int_0^\infty e^{-3y^2}dy\right) = \int_0^\infty \int_0^\infty e^{-3(x^2+y^2)} dxdy.
$$
Now change to polar coordinates to get
$$
I^2 = \int_{0}^{\pi/2} \int_0^{\infty} re^{-3r^2} dr d\theta
$$
which from here you can solve and then take the square root.
