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Today's calculation of Integral 594

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April 23, 2010
calculusintegrationgeometrycalculus computations

Problem Statement

In the xx-yy plane, two variable points P, QP,\ Q stay in P(2t, −2t2+2t), Q(t+2,−3t+2)P(2t,\ -2t^2+2t),\ Q(t+2,-3t+2) at the time tt. Let denote t0t_0 as the time such that PQ‾=0\overline{PQ}=0. When tt varies in the range of 0≤t≤t00\leq t\leq t_0, find the area of the region swept by the line segment PQPQ in the xx-yy plane.
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