- Let $\vec F = (2x+y,x)$. Let $C$ be the curve $\vec r(t) = (t,t^2)$ for $t\in [-1,2]$.
- Set up the work integral $\int_C Mdx+Ndy$.
- Compute the integral above.
- Find a function $f(x,y)$ so that $\nabla f = \vec F$. (Such a function $f$ is called a potential for $\vec F$.)
- The start point of the curve is $A=\vec r(-1)=(-1,1)$. The end point is $\vec r(2)=(?,?)$. Compute the difference in the potential from the start to the end point, so compute $f(B)-f(A)$.
- Repeat the above with $\vec F = (2y,2x-y)$ and $\vec r(t) = (3\cos t,3\sin t)$ for $t\in [0,2\pi]$.
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