Question 4 - A-Level Maths

Exam Board	AQA
Module	FP2 (Further Pure Mathematics 2)
Year	2016
Session	June
Marks	4
Topic	Integration using inverse trig and hyperbolic functions

Given that \(y = \tan ^ { - 1 } \sqrt { ( 3 x ) }\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), giving your answer in terms of \(x\).
Hence, or otherwise, show that \(\int _ { \frac { 1 } { 3 } } ^ { 1 } \frac { 1 } { ( 1 + 3 x ) \sqrt { x } } \mathrm {~d} x = \frac { \sqrt { 3 } \pi } { n }\), where \(n\) is an integer.
[0pt] [4 marks]