Question 8 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2009
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Find the equation of the tangent to the curve $y = \ln ( 3 x - 2 )$ at the point where $x = 1$.
1. Find the value of the constant $A$ such that $$\frac { 6 x } { 3 x - 2 } \equiv 2 + \frac { A } { 3 x - 2 }$$
2. Hence show that $\int _ { 2 } ^ { 6 } \frac { 6 x } { 3 x - 2 } \mathrm {~d} x = 8 + \frac { 8 } { 3 } \ln 2$.