# Math Help - Area of ellipsoid, working out the limits?

1. ## Area of ellipsoid, working out the limits?

I know the general method for this question, but I'm struggling with finding limits on $\theta$ and $\phi$

Calculate the area of the portion $E_+$ of the ellipsoid $\frac{x^2}{4}+\frac{y^2}{4}+z^2=1$ that lies above the xy plane by making use of the parameterisation $r(\theta,\phi) = (2\cos{\phi}\sin{\theta},2\sin{\phi}\sin{\theta},\ cos{\theta})$

What I've got is that because it lies above the xy plane, we have $z\geq0$ so $cos{\theta}\geq0 \implies 0\leq\theta\leq\frac{\pi}{2}$
I don't think there is any restriction on $\phi$ so we have $0\leq\phi\leq2\pi$

?

2. You may wish to consider symmetries and just work in the 1st octant.