Calculate the line integrals\\
$\int_\Gamma \vec{F}(\vec{r}) \cdot d\vec{r}$ (1)\
for the following vector fields $\vec{F}$ and paths $\Gamma$:\
a) $\vec{F} = (x^2, y, xz)$ on a line from point $P_1 = (1, -2, 2)$ to point $P_2 = (2, 1, -2)$.\
b) $\vec{F} = (\cos(x), xy)$ along the way with the parameterization $\vec{r} = (t^2, t^3)$ with $0 \le t \le 1$.\
Also make a drawing of the given path.\
c) $\vec{F} = (e^x, xy^2)$ counterclockwise along the triangle from the origin about $P_1 = (1, 0)$ to\
$P_2 = (1, 1)$ and back to the origin.\
To find the way from $\vec{r}_1$ to $\vec{r}_2$ it is easiest to parameterize along a straight line $t \in [0, 1]$\nto choose. In this case the parameterization is simply given by\
$\vec{r}(t) = \vec{r}_1 + (\vec{r}_2 - \vec{r}_1) \cdot t$ (2)
