Evaluate the surface integral of F*n (the flux) where n is the upward-pointing unit normal vector to the plane z = 3x+2 that lies within the cylinder x^2 + y^2 = 4. F = <0, 2y, 3z>
2. The attempt at a solution
The normal vector is <3,0,1> so that F*n = 3z. dS equals sqrt(10). I transform to polar coordinates and integrate 3*sqrt(10)*(3r^2*cos(theta) + 2r) over the cylinder. The answer I get is 24sqrt(10)*pi, while the correct answer is 24*pi. Does this mean that dS=1? Why?