I have found this problem in my textbook.
Evaluate $$\iint_S F\cdot n ds $$ where $$F = yz\hat i+xz\hat j+xy\hat k$$ and S is that part of the surface of the sphere $$x^2+y^2+z^2 = 1$$ which lies in first octant.
I have tried to solve this problem using $x = rcos\theta \cdot sin\phi $ and $y = rsin\theta \cdot sin\phi$ . But i'm stuck in determining the limit. In my text book they used $\phi : 0\to\pi/2$ and $\theta : 0\to\pi/2$ . But i couldn't understand it. Can anyone please explain it? Thanks in advance.