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[Solution Library] Consider the differential form w=((y)/(x^2y^2+1)-1)dx+((x)/(x^2y^2+1)-1)dy Show that w is an exact form Use the preceding part evaluate ∫_Cw

Question: Consider the differential form

\[w=\left( \frac{y}{{{x}^{2}}{{y}^{2}}+1}-1 \right)dx+\left( \frac{x}{{{x}^{2}}{{y}^{2}}+1}-1 \right)dy\]
  1. Show that \(w\) is an exact form
  2. 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).
  3. Evaluate \(\int\limits_{C}{w}\) directly, by parametrizing the path

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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