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Calculus Level 5

Evaluate : \[\oint_{C}y^{2}dx +x^{2} \, dy\]

where \(C\) is the closed curve which is the boundary of the triangle with vertices \((0; 0)\), \((1; 1)\) and \((1; 0)\), with the counterclockwise orientation.

Give your answer correct to 3 decimal places.

Bonus: Try to solve it without Greens' Theorem.


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