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Today's calculation of Integral 124

Source: Kwansei University entrance exam 2006

July 11, 2006
calculusintegrationgeometrytrigonometryderivativecalculus computations

Problem Statement

Let a>1.a>1. Find the area S(a)S(a) of the part surrounded by the curve y=a4(a2−x2)3 (0≤x≤1), xy=\frac{a^{4}}{\sqrt{(a^{2}-x^{2})^{3}}}\ (0\leq x\leq 1),\ x axis , yy axis and the line x=1,x=1, then when aa varies in the range of a>1,a>1, then find the extremal value of S(a).S(a).
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