1. Consider the curve C in the xy-plane given by (x(t), y(t)) = (a(1 - cost) cost, a(1 - cost) sint), 0 ≤t≤2π, where a is a fixed positive number. Write r(t) = x(t)i+y(t)j. 1. Sketch the curve C, and calculate dr(t) and dr(t) dt dt 2. Calculate the arc length of C. : 3. Calculate the line integral √ F. dr for F = −yi + xj. [Warning: You are NOT allowed to pick a value for a in your solution.]

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