Let C be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤ π/2. (a) Give a parametrization of C. (Hint: Start with the generic r(t) = (x, y), writer and y in polar coordinates, then use the fact that r = 0 along C) (b) Compute the line integrala arctan (2) ds. (c) Consider the vector field F(x, y) = (x²² - y³, 2³). Is F conservative? (d) Compute the flow/F.dr (with F the vector field from part (e)) indirectly by considering

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