MathDB
Today's calculation of Integral 328

Source: 2008 Osaka University entrance exam/Science

May 28, 2008
calculusintegrationgeometrygeometric transformationrotationcalculus computations

Problem Statement

Let t t be a negative real number and D D be the part bounded by the curve y\equal{}2^{2x\plus{}2t}, the curve y\equal{}2^{x\plus{}3t} and the y y axis. (1) Find the volume V(t) V(t) generated by rotation of D D about the x x axis. (2) When t t moves in the range of negative real number, find the maximum value of V(t) V(t).