The domain of f(x, y) is the xy-plane, and values of f are given in the table below.
y\x 0 1 2 3 4
0 55 55 55 55 57
1 56 57 57 59 60
2 59 62 65 66 67
3 57 56 56 56 56
4 60 60 62 64 65
Find $\int_C \text{grad } f \cdot d\mathbf{r}$, where $C$ is
(a) A line from (0, 1) to (2, 2).
$\int_C \text{grad } f \cdot d\mathbf{r} =$
(b) A circle of radius 1 centered at (2, 1) traversed counterclockwise.
$\int_C \text{grad } f \cdot d\mathbf{r} =$
