Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ where $C$ is the portion of the circle centered at the origin with radius $2$ in the $1^{st}$ quadrant with counter clockwise rotation and

vec$(F)(x,y)=(2xy-4-\frac{1}{2}sin(\frac{1}{2}x)sin(\frac{1}{2}y))vec(i)+(x^2+\frac{1}{2}cos(\frac{1}{2}x)cos(\frac{1}{2}y))vec(j)$