Evaluate the integrals in simplest way possible ∬P (dot)n ds over upper half of the sphere r = 1 if P = curl (jx-kz)

but if divergence theorem is used
del cross del dot y = 0
y=(jx-kz)

so whats the possible way to solve this without using divergence theorem?
pls help...

Question

Evaluate the integrals in simplest way possible ∬P (dot)n ds over upper half of the sphere r = 1 if P = curl (jx-kz)

but if divergence theorem is used 
del cross del dot y = 0
y=(jx-kz)

so whats the possible way to solve this without using divergence theorem?
pls help...

anonymous · Answer

pls help me with thgis question..... i dont get this, how will i express the volume integral in double integrals......

anonymous · Answer

Curl (0,x,-z) = (0,0,1) 

n ds = (x/z, y/z, 1) dA 

∬ dA 
where A is the disk x^2 + y^2 <= 1 
= pi 

but its a sphere, how can i write x^2 + y^2 <= 1