- #1

- 402

- 1

my problem here is to find a general way for setting the differential surface part (ds) from the integral

if [tex]\vec{F}[/tex] was a vector field defined as:

[tex]\vec{F} = x^3\vec{i} + y^3\vec{j} + z^2\vec{k}[/tex]

[tex]\vec{i},\vec{j},\vec{k}[/tex] Unit Vectors for axes [tex]x,y,z[/tex]

Evaluate:

[tex] \oint_{s} \vec{F}\cdot\vec{ds} [/tex]

While s is the area of the volume bounded with equation surfaces:

[tex]z=0, z=1-(x^2+y^2)[/tex]

the answer will be [tex]\frac{5\pi}{6}[/tex]

PLEASE DON'T USE THE THEOREM:

[tex]\int\int\int_{V}\vec{\nabla}\cdot\vec{F}\cdot dV[/tex]