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Please make sure to do both parts (a) and (b). Try to show all steps. Thanks!
8. Let \( \m ...
Please make sure to do both parts (a) and (b). Try to show all steps. Thanks!
8. Let \( \mathrm{C} \) be the boundary curve of the triangle with vertices \( \mathrm{P}(-1,0), Q(0,1) \), and \( \mathrm{R}(1,1) \). Let \( \mathrm{C} \) be oriented counter-clockwise. Draw triangle \( \mathrm{PQR} \) and find \( \int_{C} y^{2} d x-x^{2} d y \) (a) directly, as a line integral AND (b) as a double integral, by using Green's Theorem.