A force $\vec F = (y\,\hat i + 2x\,\hat j)\ \text{N}$, where $x$ and $y$ are the coordinates in metres, acts on a particle. The particle moves from the origin O to the point P $(2\ \text{m},\ 2\ \text{m})$ along the parabola $y = \dfrac{x^2}{2}$, as shown in the figure. How much work does the force do?

Fig. 1: Axes x and y in metres, each from 0 to about 2.4. A blue curve y = x squared over 2 runs from the origin O to the point P at 2 m, 2 m, with an arrow showing travel from O towards P.