Question #2003104: General Differentiation


Question: Verify Stoke’s Theorem by evaluating \[\iint\limits_{C}{\ F\ \cdot \ T\ d\,S}\] as a line integral:

\[\begin{align}
& F\,\left( \,x,\ y,\ z\, \right)\quad =\quad \left( \,-\,y\ +\ z\, \right)\ i\quad +\quad \left( \,x\ -\ z\, \right)\ j\quad +\quad \left( \,x\ -\ y\, \right)\ k \\
& \\
& S:\quad z\ =\ 4\ -\ {{x}^{\,2}}\ -\ {{y}^{\,2}},\ 0\ \le \ z \\
\end{align}\]

Solution: The solution consists of 262 words (2 pages)
Deliverables: Word Document

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