- Let $C$ be the right half $x\geq 0$ of a circle of radius 5. Compute the line integral $\ds \int_C xds$.
- Find the average value of $T(x,y,z)=x^2+y^2+z$ along the helix $\vec r(t)=(3\cos t,3\sin t, 4t)$ for $0\leq t\leq 2\pi$. Recall that average value is $\bar T=\ds\frac{\int_C Tds}{\int_Cds}.$
- Let $\vec F = (-y,x+y)$ and $C$ be the straight line segment from $(2,0)$ to $(0,2)$.
- Compute $\ds\int_C Mdx+Ndy$.
- Compute $\ds\int_C Mdy-Ndx$.
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