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1.  Evaluate \(\int_C x^2+y^2 ds\), where \(C:\vec{r}(t) = \langle \cos t, \sin t \rangle\), \(0 \leq t \leq 2\pi\) (If you think about this, you can save yourself some work).

a.  0

b.  1

c.  2

d.  \(\pi\)

e.  \(2\pi\)

2.  Evaluate \(\int_C \langle e^x, xy \rangle \cdot d\vec{r}\), where \(C:\vec{r}(t) = \langle t^2, t \rangle\), \(0 \leq t \leq 1\)

a.  \(e + \frac{1}{4}\)

b.  \(e^2\)

c.  \(e - \frac{3}{4}\)

d.  \(e^2 + \frac{1}{4}\)

e.  \(1\)

3.  Evaluate \(\int_C \langle -y, x\rangle \cdot d\vec{r}\), where \(C:\vec{r}(t) = \langle \cos t, \sin t \rangle\), \(0 \leq t \leq 2\pi\) (If you think about this, you can save yourself some work).

a.  \(-4\pi\)

b.  \(-2\pi\)

c.  0

d.  \(2\pi\)

e.  \(4\pi\)

4.  Describe the following surface \(S: \vec{r}(u,v) = \langle v\cos u, v\sin u, v\rangle\) where \(0 \leq u \leq 2\pi\), and \(0\leq v\leq 1\).

a.  A finite circular cylinder

b.  An infinite circular cylinder

c.  A finite cone

d.  An infinite cone

e.  A hemisphere