Task: Calculate the line integral F*T ds around C where F=(-xz-2y,x^2-yz,z^2+1) and C is the boundary curve between the cylinder x^2+Y^2=1 and the top half of the sphere X^2+Y^2+z^2=10. My work: Surely I'm supposed to use Stoke's theorem here. First I replace x^2+y^2 with 1 in the sphere equation, to find that C lies in the plane z=3. Then I need the normal unit vector. But how do I find that? Is it simply the partial of the surface eq. f(x,y,z)=x^2+y^2+z^2-10=0?