To find the work done by the force $$F(x,y) = \left \langle 7y -7xe^{14x},\tan^{-1}(14y)-4x \right \rangle$$ moving an object counterclockwise along the boundary of the triangle formed by the points $(0,0),(1,0),(1,4)$.
Here I used Green's Theorem:
$$W = \int P \, dx + Q \, dy = \iint \frac{\delta Q}{\delta x} - \frac{\delta P}{\delta y} \, dA = \int_0^1 \int_0^{4x} -11\, dy \, dx = -22.$$
Is the solution correct?