Calculus 2 Quiz
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PARAMETRIC, POLAR & VECTOR FUNCTIONS
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To find the area of the region bounded by the parabola y=x2y=x^2 and the line y=4y=4, a student parameterizes the parabola as x(t)=t,y(t)=t2x(t)=t, y(t)=t^2 for t∈[−2,2]t \in [-2,2]. They propose the integral ∫−22(4−t2) dt\int_{-2}^2 (4 - t^2) \, dt. What is the implicit assumption made in this setup?
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