- #1
physmatics
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Homework Statement
Calculate the surface integral I = [tex]\int\int[/tex] f dS of the function f(x,y,z) = [tex]\sqrt{1/2 + y^{2}}[/tex] over the surface S given by [tex]x^{2} + 2*y^{2} = 1[/tex], [tex]0 \leq z \leq x^{2} + y^{2}[/tex]. (Clue: parametrize the surface.)
Homework Equations
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The Attempt at a Solution
The surface is, as far as I can tell, the elliptic cylinder [tex]x^{2} + 2*y^{2} = 1[/tex], from z = 0 to z = 1.
Now, I have trouble parametrizing the surface. Can I just parametrize it as an ellips in [tex]R^{2}[/tex]? The equation of that ellips would be [tex]x = \sqrt{1 - 2*y^{2}}[/tex]. Then, how do I parametrize the ellips given the equation? And also, why is 'parametrizing the surface' a clue? I really don't get it...
Sorry for clumsy use of LaTeX, I'm not very familiar with it.
Thank you very much!