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Surface Integrals Prolbem? If the mass per unit area of a surface is given by ρ=xy, find the mass if S is the part of the cylinder x^2+z^2=25 which is in the first octant and contained within the cylinder x^2+y^2=16.
So here was my attempt.
I parametrized the curve.
x^2+z^2=25
r(u, v) = <5cos(u), v, 5sin(u)>
I then plugged into the...

Respuesta :

LammettHash
You're trying to find the mass of the region, so a triple integral is probably more appropriate here.

[tex]\displaystyle\text{mass}_S=\iiint_S\rho(x,y,z)\,\mathrm dV=\int_0^4\int_0^{\sqrt{16-x^2}}\int_0^{\sqrt25-x^2} xy\,\mathrm dz\,\mathrm dy\,\mathrm dx=\frac{706}5[/tex]

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