Today's calculation of Integral 494
Source: 1988 Nippon University entrance exam/Architecture
October 9, 2009
calculusintegrationconicshyperbolaanalytic geometrycalculus computations
Problem Statement
Suppose the curve C: y \equal{} ax^3 \plus{} 4x\ (a\neq 0) has a common tangent line at the point with the hyperbola xy \equal{} 1 in the first quadrant.
(1) Find the value of and the coordinate of the point .
(2) Find the volume formed by the revolution of the solid of the figure bounded by the line segment and the curve about the line .
[Edited.]