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Surface Integral of Two Surfaces

  1. Dec 12, 2004 #1
    Hello!

    This is a question from one of our past exams, and it's had me stumped for the past hour. The question states:

    The cylinder [tex]x^2+y^2=2x[/tex] cuts out a portion of a surface S from the upper nappe of the cone [tex]x^2+y^2=z^2[/tex].

    Compute the surface integral: [tex]\int\int (x^4-y^4+y^2z^2-z^2x^2+1) dS[/tex]

    I'm mainly having trouble getting started. What exactly is the surface that we're supposed to evaluate the integral over?

    My guess on this question is that I should parametrize the cone:
    [tex]T(u,v) = (vcosu, vsinu, v)[/tex]

    And use that to find [tex]T_u X T_v[/tex].

    But what do I do after this? In order to find the limits of integration for u and v, do I use the conditions given by the cylinder? [tex]v = 2cosu[/tex]?

    Using that still doesn't give me the numerica limits for v, though.

    Help, anyone?
     
    Last edited: Dec 12, 2004
  2. jcsd
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