10. Define the two curves $C_1$ and $C_2$ by
$C_1: \vec{r}(t) = (\cos(t), 1, \sin(t))$, $0 \le t \le 2\pi$,
$C_2: \vec{r}(t) = (\sin(t), \cos(t), t + 1)$, $0 \le t \le 2\pi$,
and define the two vector fields $\vec{F}$ and $\vec{G}$ by
$\vec{F}(x, y, z) = (0, z, 0)$,
$\vec{G}(x, y, z) = (e^x, 3y^2, \frac{1}{z^2 + 1})$
Evaluate the following. (Which ones can you use shortcuts for?)
(a) $\oint_{C_1} \vec{F} \cdot d\vec{r}$
(b) $\oint_{C_1} \vec{G} \cdot d\vec{r}$
(c) $\oint_{C_2} \vec{F} \cdot d\vec{r}$
(d) $\oint_{C_2} \vec{G} \cdot d\vec{r}$
