LyraDaBraccio Posted September 14, 2012 Share Posted September 14, 2012 I was having a looks at multiple integrals, line/surface/volume integrals and the like the other week, and decided to try some problems, but this one stumped me: [math] \int \int_S xz\mathbf{i} + x\mathbf{j} + y\mathbf{k}\: \textrm{d} S [/math] where S is the unit hemisphere of radius 9 for y >= 0 I thought I could change the variables to spherical co-ordinates, but I don't see how that would work with the particularly nasty stuff you'd get for the [math] \sqrt{\left( \frac{\partial z}{\partial x} \right) ^2 + \left( \frac{\partial z}{\partial y} \right) ^2 +1} [/math] along with the square roots necessary in writing z in terms of x and y. Basically this confused the heck out of me and I'd appreciate any help Link to comment Share on other sites More sharing options...
MindShadowfax Posted December 3, 2012 Share Posted December 3, 2012 (edited) I'm not 100% about what I'm going to say as this is what i'm studying myself but take a look at this.. When you have the first int you posted then you would get IntInt(F(r(u,v) |N|) dS right? that's doing F=<xz;x;y> and looking at the surface with a parametric equation. Then you can use the Gauss Theorem Gauss int intF n dS = int int int div F dV And that is way easier. Sorry about the way i wrote the equations I don't know how to do it in a proper way. Anyway I'd do that Good luck Edited December 3, 2012 by MindShadowfax Link to comment Share on other sites More sharing options...
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