On the next exam I'm supposed to show that ∫e^(-x^2)dx = √(π/2).
The Attempt at a Solution
When the professor was showing us one way to do it, I remember him doing a step that was like
∫e^(-x^2)dx ∫e^(-x^2)dx = ∫∫e^(-x^2 - y^2) dx dy.
Is that legal? I never knew ∫f(x)dx ∫g(y)dy = ∫∫f(x)g(y) dx dy.