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mit_hacker
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Homework Statement
(Q) Compute the surface integral g = xy over the triangle x+y+z=1,
x,y,z>=0.
Homework Equations
The Attempt at a Solution
The triangular region basically means that the region in consideration is a
plane and not a sphere, cylinder etc...
Therefore, we can let the region r be defined as r = xi + yj + (1-x-y)k.
thus, partial derivative of r w.r.t x = i-k and that w.r.t y = j-k.
their cross product comes to -i+j+k. the modulus of this is of course
sqrt(3).
So the double integral will be the double integral over region R of
sqrt(3)xydA.
the problem is, I have no idea as to how I can find the limits of this
double integral.
Please advice.
Thank-you very much for your time and effort!