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A man is pushing a cart with a mass of $13\:kg$ across a hill of varying gradient. As a result the force he must apply to the cart varies with position as $F = mg\frac{x}{y}\,\hat{i} + mg\frac{y}{x}\,\hat{j}$. He starts at a position of $(0.0\:m, 1.0\:m)$, pushes the cart $5.2\:m$ in the $x$-direction, then turns a corner and pushes the cart $2.9\:m$ in the $y$-direction.

What is the total work (in J) done by the man in pushing the cart?

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