CAIE P1 2011 June — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionJune
TopicIntegration by Substitution

7 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 3 } { ( 1 + 2 x ) ^ { 2 } }\) and the point \(\left( 1 , \frac { 1 } { 2 } \right)\) lies on the curve.
  1. Find the equation of the curve.
  2. Find the set of values of \(x\) for which the gradient of the curve is less than \(\frac { 1 } { 3 }\).