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Today's calculation of Integral 809

Source: 2012 Kobe University entrance exam/Humanities

March 16, 2012
calculusintegrationgeometryconicsparabolacalculus computations

Problem Statement

For a>0a>0, denote by S(a)S(a) the area of the part bounded by the parabolas y=12x2−3ay=\frac 12x^2-3a and y=−12x2+2ax−a3−a2y=-\frac 12x^2+2ax-a^3-a^2. Find the maximum area of S(a)S(a).
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