I have two problems on surface integrals. 1] I have a constant vector [itex]\vec v = v_0\hat k[/itex]. I have to evaluate the flux of this vector field through a curved hemispherical surface defined by [itex]x^2 + y^2 + z^2 = r^2[/itex], for z>0. The question says use Stoke's theorem. Stoke's theorem suggests: [tex]\int_s \left(\vec \nabla \times \vec v\right) \cdot d\vec a = \int_p \vec v \cdot d\vec l[/tex] But the curl of this vector comes out to be zero :yuck:. Am I going right? How is the surface integral evaluated? 2] I have a vector field [itex]\vec A = y\hat i + z\hat j + x\hat k[/itex]. I have to find the value of the surface integral: [tex]\int_s \left(\vec \nabla \times \vec A\right) \cdot d\vec a[/tex] The surface S here is a paraboloid defined by: [tex]z = 1 - x^2 - y^2[/tex] I evaluated the curl and it comes out to be: [tex]\vec \nabla \times \vec A = -1\left(\hat i + \hat j + \hat k\right)[/tex] I need help here on the procedure to evaluate the surface integral.