Word Count : 338

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To evaluate the line integral \(\oint_{C}(y^{3}dx - x^{3}dy)\) using Green's Theorem, we can express the given integral as: \[ \oint_{C} P(x, y)dx + Q(x, y)dy \] Where: - \(P(x, y) = y^3\) - \(Q(x, y) = -x^3\) According to Green’s Theorem, we have: \[ \oint_{C} P(x, y)dx + Q(x, y)dy = \iint_{D} \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) dA \] Where \(D\) is the ____ ____ ____ _______ ____ _________ _____ __________ ________ ____.
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