AQA C2 2010 January — Question 2

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2010
SessionJanuary
TopicStandard Integrals and Reverse Chain Rule

2 At the point \(( x , y )\) on a curve, where \(x > 0\), the gradient is given by $$\frac { \mathrm { d } y } { \mathrm {~d} x } = 7 \sqrt { x ^ { 5 } } - 4$$
  1. Write \(\sqrt { x ^ { 5 } }\) in the form \(x ^ { k }\), where \(k\) is a fraction.
  2. Find \(\int \left( 7 \sqrt { x ^ { 5 } } - 4 \right) \mathrm { d } x\).
  3. Hence find the equation of the curve, given that the curve passes through the point \(( 1,3 )\).