Hello, I am looking for someone to check my work for me. Please see the attached questions and my work. It deals with surface area and parametric representations.
Your solutions to problem 1 and 2.1 are correct. For 2.2 you have calculated "dS" using the length of the normal vector at the single point (4,−2,0) where u= 2 and v=π. You can't do that. It has to be at any u, v. So dS=u2+4u2cos2(v)+4u2sin2(v)dudv=5u2dudv=u5dudv. Yes, x(y2+z2)=2u(u2cos2(v)+u2sin2(v))=2u(u2)=2u3 (it seems more work that necessary to do it as xy2+xz2). So the integral is 25∫02π∫03u4dudv.
For problem 3 you have one notational errors, perhaps a "typo". You have "dS=14" when it should be, of course, dS=14dxdy. But you do have the correct integral.
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