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Today's calculation of Integral 691

Source:

April 16, 2011
calculusintegrationlogarithmsgeometrygeometric transformationrotationcalculus computations

Problem Statement

Let aa be a constant. In the xyxy palne, the curve C1:y=ln⁡xxC_1:y=\frac{\ln x}{x} touches C2:y=ax2C_2:y=ax^2. Find the volume of the solid generated by a rotation of the part enclosed by C1, C2C_1,\ C_2 and the xx axis about the xx axis.
2011 Yokohama National Universty entrance exam/Engineering
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