One of the question in my homework asks to verify that the surface are of
$ \mathbf{r} = a(1+\cos\phi)\sin\phi \cos\theta \mathbf{i} + a(1+\cos\phi)\sin\phi \sin\theta \mathbf{j} + a(1+\cos\phi)\cos\phi \mathbf{k}$
is $\frac{32}{5}\pi a^2$
I started with the equation to the area of the surface being the double integral of $|\mathbf{r}_{\phi} \times \mathbf{r}_{\theta}|$... but MAN this is so long it's almost unworkable. Am I doing this the stupid way? Can this be simplified?
All I can tell is that $\mathbf{r} = a\sin\phi \cos\theta \mathbf{i} + a\sin\phi \sin\theta \mathbf{j} + a\cos\phi \mathbf{k}$ is te equation of a sphere of radius $a$, but you can't really factor out areas, that I know of... so I don't see how this helps.