Today's calculation of Integral 298
Source: 2008 Keio University entrance exam/Science and Technology
February 16, 2008
calculusintegrationgeometryalgebrabinomial theoremcalculus computations
Problem Statement
Let be the region : \left\{(x,\ y)|x\geq 0,\ y\geq 0, \left(\frac{x}{a}\right)^{\frac{1}{2}}\plus{}\left(\frac{y}{1\minus{}a}\right)^{\frac{1}{2}}\leq 1\right\} for
(1) Find the area of
(2) Find the maximum volume of the solid obtained by revolving around the axis.