1. The problem statement, all variables and given/known data I have to control stokes theorem( I have to calculate line-and surface integral. I have a vectorfield a=(3y,xz,yz^2). And surface S is a paraboloid 2z=x^2+y^2. And it is limited by plane z=2. For line integral the line is a circle C: x^2+y^2=4 on the plane z=2. Vector n is pointing down ( Outwards). [Broken] 2. Relevant equations The line integral i got . it is -4*pi. http://en.wikipedia.org/wiki/Stokes_theorem 3. The attempt at a solution Okay so i get these wierd answers for surface integral and it should be -4 * pi. I have done it in 5 different ways. I find Flux a =(z^2-x,0,z-3) and then i find the n*dS. n*dS=-(f_x,f_y,1) = (x,y,-1) dx dy Lets say that i use cylindrical coordinates , then x=r*cos t, y=r*sin t and z=z. I find z = (x^2+y^2)/2 so it will be z=r^2/2 I think about the bonds , they should be 0 ≤ r ≤ 2 and 0 ≤ t ≤ 2*pi Then i find the double integral →∬(z^2-x,0,z-3)*(x,y,-1) dx dy= ∬ z^2x-x^2-z+3 dS= ∬(r=0 to 2, t=0 to 2pi) r^4/4*r*r*cos t - r^2*r*(cos t)^2-r^2/2*r-3r dt dr = ∫(r=0 to 2) r^6/4 * sin t - r^3(t/2-1/2*cos t*sin t)-r^3/2*t+3rt dr= ∫(r=0 to 2) 0-r^3*pi - 0 - r^3* pi +6 r pi dr= = ∫(r=0 to 2) -2*r^3* pi + 6*r*pi = -8*pi +12 * pi = 4 * pi So i get 4 * pi from surface integral and -4*pi from line integral. Can anyone explain what am i doing wrong ?