CAIE P1 2004 November — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2004
SessionNovember
TopicVolumes of Revolution

10 A curve has equation \(y = x ^ { 2 } + \frac { 2 } { x }\).
  1. Write down expressions for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
  2. Find the coordinates of the stationary point on the curve and determine its nature.
  3. Find the volume of the solid formed when the region enclosed by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 2\) is rotated completely about the \(x\)-axis.