Verification that the two sides of Stokes' theorem agree;
Exploration of the freedom to choose any surface whose boundary is the given curve.
Evaluate \(\oint\boldsymbol{\vec{F}}\cdot d\boldsymbol{\vec{r}}\) explicitly as a line integral, where
\(\boldsymbol{\vec{F}} = r^3 \,\boldsymbol{\hat{\phi}}\) and \(C\) is the circle of radius \(3\) in the \(xy\)-plane,
oriented in the usual, counterclockwise direction (as seen from above).
Stokes' Theorem
List at least 3 different surfaces which you could use with Stokes' Theorem to evaluate the line integral in the previous problem.
Evaluate the surface integral for any one of the surfaces on your list.
If time permits, evaluate the surface integral for other surfaces on your
list.