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Today's calculation of Integral 569

Source: 2010 Kyoto University entrance exam/Humanities, Problem 1 (1)

February 26, 2010
calculusintegrationanalytic geometrygeometrygraphing linesslopeconics

Problem Statement

In the coordinate plane, denote by S(a) S(a) the area of the region bounded by the line passing through the point (1, 2) (1,\ 2) with the slope a a and the parabola y\equal{}x^2. When a a varies in the range of 0≤a≤6 0\leq a\leq 6, find the value of a a such that S(a) S(a) is minimized.
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