- Compute the work done by $\vec F = (4y,-4x)$ along the circle $\vec r(t) = (3\cos t, 3\sin t).$
- Compute this work using $ \oint_{C} M dx+Ndy$.
- Compute this work using $\iint_R N_x-M_y dA$.
- Compute the work done by $\vec F = (2x-y,2x+4y)$ along the triangle with corners $(0,0)$, $(2,0)$, and $(0,3)$.
- Set up the single double integral $\iint_R N_x-M_y dA$.
- Set up three integrals needed using $ \oint_{C} M dx+Ndy$.
- Evaluate one of the formulas above to actually find the work.
- Consider the surface parametrized by $\vec r(u,v) = (u, v, u^2+v^2)$ for $-3\leq u\leq 3$ and $0\leq v\leq 3$.
- Draw the surface.
- Compute $d\sigma = \left |\dfrac{\partial \vec r}{\partial u}\times\dfrac{\partial \vec r}{\partial v}\right|dudv$.
- Set up an integral to compute the surface area of the surface.
- Set up an integral formula to compute $\bar z$ for this surface.
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