find the area of the cylinder x^2+z^2=a^2 that is inside the cylinder x^2+y^2=a^2. my attempt: parameterise x^2+z^2=a^2 as a vector r(x,y) = (x,y,(a^2-x^2)^1/2). using the formula given here : http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx, I found the surface area = the double integral of a(a^2-x^2)^-1/2 dxdy, over the circle x^2+y^2=a^2 on the x-y plane. change variables into polar coordinates, so we obtain the double integral of a(a^2-(r cos (u))^2)^-1/2 rdrdu, for 0<r<a, 0<u<2pi. Solving this i get zero, which doesnt seem right. where did i go wrong?