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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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