Difficult# Work in a Non-Uniform Field

CLMECH-H5BNEB

Imagine an external force field is described by $\vec{F}\left(\vec{r}\right) = (y^2\hat{i})\,N$, where $\vec{r} = (x\hat{i} +y\hat{j})$ is the position.

How much work is done pushing against this force to move along a straight line from the point (0, 0) to (-4.0, 2.0)?