Use Stokes' Theorem to Evaluate Where F(x, Y, Z) $\sigma$

question 124

Essay

Use Stokes' Theorem to evaluate where F(x, y, z) = 3y i and $\sigma$ is that portion of the ellipsoid 4x² + 4y² + z² = 4 for which z $\ge$ 0.

---

Definitions:

Tetrahedral Geometry

A molecular geometry where a central atom is surrounded by four atoms placed at the corners of a tetrahedron.

Ethylene Glycol

A toxic, colorless liquid used as antifreeze in cooling and heating systems.

Carbon Atoms

The chemical element with atomic number 6, forming the basis of organic life with its ability to form stable, complex molecules.

Secondary Amine

An organic compound where two alkyl or aryl groups are attached to the same nitrogen atom, not including the hydrogen.