- #1
Saladsamurai
- 3,020
- 7
Homework Statement
Evaluate the surface Integral [tex]I=\int\int_S\vec{F}\cdot\vec{n}\,dS[/tex]
where [tex]\vec{F}=<z^2+xy^2,x^100e^x, y+x^2z>[/tex]
and S is the surface bounded by the paraboloid [itex]z=x^2+y^2[/itex]
and the plane z=1; oriented by the outward normal.
The Attempt at a Solution
[tex]I=int\int_S\vec{F}\cdot\vec{n}\,dS=\int\int\int_E(div\vec{F})dV[/tex]
[tex](div\vec{F})=y^2+x^2[/tex]
[tex]\Rightarrow I=\int\int_D(\int_{z=x^2+y^2}^1(x^2+y^2)\,dz)\,dA[/tex]
[tex]\Rightarrow I=\int\int_D(1-(x^2+y^2)\,dA[/tex]
Is it just Polar Coordinates all the way home now?
Thanks,
Casey