MathDB

124

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 124

Source: Kwansei University entrance exam 2006

7/11/2006
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).
calculusintegrationgeometrytrigonometryderivativecalculus computations