How can I correctly solve for dA in Gauss's Law for a sphere?

[Rib5]

Hey, I'm having some trouble solving for the dA portion of Guss's Law for a sphere as the Gaussian surface and a point charge on the inside.

According to my book, Integral(1dA) = 4(pi)r^2

So when I try to integrate it myself I get 2(pi^2)r^2
The integral I solve is \int\int r\phi r\theta where theta = [0,2pi] and phi = [0,pi]

Can anyone set me straight please?

 

[jtbell]

On the surface of a sphere, the element of area bounded by d\theta and d\phi has area (r d\theta)(r \sin \theta d\phi) = r^2 \sin \theta d\theta d\phi.