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{
\bf ``QUIZ'' for Nov. 9, 2009
}
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{\bf NAME:} (print!) $\underline
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{\quad \bf Section:}
$\underline{\quad\quad\quad}$

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{\bf E-MAIL ADDRESS:} (print!) 
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{\bf 1.} 

Determine whether or not the vector field 
$$
F(x,y,z)=y^2z^3 \, {\bf i} + 2xyz^3 \, {\bf j} + 3xy^2z^2\, {\bf k} 
$$ 
is conservative. If it is conservative, find a function $f$ such that
${\bf F}=\nabla f$.

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{\bf 2.} 
Show that the line integral
$$
\int_C 2xy^2 \, dx \, + \, 2x^2y \, dy \quad ,
$$
is independent of the path $C$, and evaluate it if
$C$ is {\it any} path from $(1,0)$ to $(0,1)$.


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