Let $\omega = (xyz)dx +(xy^2)dy + (e^x)dz$
Evaluate $\int_S d\omega$ where $S$ is the cone with base $x^2+y^2 = 9$ in the xy plane and vertex at $(-2,3,1)$ oriented by the normal which points away from the center line.
I am thinking of using the generalized Stokes theorem, so I am trying to find the $dS$ that bounds my surface; but I am having trouble parametrizing this boundary.. how do I parametrize this 2D shape?
The cone is a surface of revolution $\frac{x^2}{a^2}+ \frac{y^2}{b^2} = \frac{z^2}{c^2}$
2026-04-01 02:00:04.1775008804
Evaluate the surface integral over a cone region
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