CAIE FP1 2014 June — Question 8

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicParametric equations

8 The curve \(C\) has parametric equations $$x = t ^ { 2 } , \quad y = t - \frac { 1 } { 3 } t ^ { 3 } , \quad \text { for } 0 \leqslant t \leqslant 1 .$$ Find
  1. the arc length of \(C\),
  2. the surface area generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.