3. Refer to the star-shaped region R.
(4,7)
(3,5)
(5,5)
(1,4)
(7,4)
(3,3)
(5,3)
(4,1)
(a) Let C be the path from (5,5) to (4,7). Find
$\int_C (2\vec{i} + 13\vec{j}) \cdot d\vec{r}$
(b) Let C be the path from (5,5) to (4,7). Find
$\int_C (4x\vec{i} + 3y\vec{j}) \cdot d\vec{r}$
(c) Let C be the path from (5,5) to (4,7). Find
$\int_C ((4x + 5y)\vec{i} + (2x + 3y)\vec{j}) \cdot d\vec{r}$
(d) Let C be the path around the outside of the star, traced counterclockwise. Find
$\int_C ((4x + 5y)\vec{i} + (2x + 3y)\vec{j}) \cdot d\vec{r}$