With each problem today, don't worry about completing each integral. Instead, set up each integral in terms of $t$, and then move to the next.
- Let $C$ be the right half $x\geq 0$ of a circle of radius 5. Set up the line integral $\ds \int_C xds$.
- Let $T(x,y,z)=x^2+y^2+z$ and the curve $C$ be parametrized by $\vec r(t)=(3\cos t,3\sin t, 4t)$ for $0\leq t\leq 2\pi$. That average value is given by $\bar T=\ds\frac{\int_C Tds}{\int_Cds}.$ Set up this integral.
- Let $\vec F = (-y,x+y)$ and $C$ be the straight line segment from $(3,0)$ to $(0,2)$.
- Set up the work integral $\ds\int_C Mdx+Ndy$.
- Set up the flux integral $\ds\int_C Mdy-Ndx$.
- Repeat the previous part with $\vec F = (2x+y,3x)$ for the curve $x=y^2$ from $(1,-1)$ to $(4,2)$.
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