Question: Consider the differential form

\[w=\left( \frac{y}{{{x}^{2}}{{y}^{2}}+1}-1 \right)dx+\left( \frac{x}{{{x}^{2}}{{y}^{2}}+1}-1 \right)dy\]

(a) Show that \(w\) is an exact form

(b) Use the preceding part evaluate \(\int\limits_{C}{w}\) where C is the path consisting of line segments starting at (1, 1), continuing to (2, 2), then (3, 1) and ending at (4, 3).

(c) Evaluate \(\int\limits_{C}{w}\) directly, by parametrizing the path