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Today's calculation of Integral 292

Source: 2008 Tokyo University of Science entrance exam/Science and Enginnering

February 7, 2008
calculusintegrationgeometryparameterizationconicshyperbolacalculus computations

Problem Statement

Let x, y x,\ y and t t be real numbers such that {t3−(2y−1)t2−t+2y−1=0emsp;xt−2t+2y=0emsp; \{ \begin{array}{ll} t^3 - (2y - 1)t^2 - t + 2y - 1 = 0 &   \\ xt - 2t + 2y = 0 &   \end{array} In x−y x - y plane find the area of the figure bounded by the part of curves above with x≥0 x\geq 0 and the line y=2. y = 2.
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