Find the value of

\[ \displaystyle I=\int_{C} x^{2}dy - y^{2}dx \]

where \( C: \dfrac{x^{2}}{4} + \dfrac{y^{2}}{9} =1 , 2 \ge x \ge 0 , 3 \ge y \ge 0 \), oriented from \((2,0)\) to \((0,3)\).

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