I saw this, and I don't understand why this is allowed:

∫(θ = 0 to 2π) ∫(r = 0 to ∞) e^(-r^2) * r dr dθ

Both the same integral split apart into two:

∫(θ = 0 to 2π) dθ * ∫(r = 0 to ∞) e^(-r^2) * r dr

Question

I saw this, and I don't understand why this is allowed:

∫(θ = 0 to 2π) ∫(r = 0 to ∞) e^(-r^2) * r dr dθ

Both the same integral split apart into two:

∫(θ = 0 to 2π) dθ * ∫(r = 0 to ∞) e^(-r^2) * r dr

anonymous · Answer

I don't understand what you're saying. You've written the same integral twice except forgotten the d theta the second time. And theta doesn't appear in the integral, so I wonder why you'd want to integrate over it, really. it's just a constant.

anonymous · Answer

look at the original definition for double integrals in Riemann sums...

kainui · Answer

I'm teaching myself calculus, so I don't know the original definition or why it's acceptable.