Question 7 - A-Level Maths

Exam Board	Edexcel
Module	Paper 1 (Paper 1)
Year	2018
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Given that \(k \in \mathbb { Z } ^ { + }\)
1. show that \(\int _ { k } ^ { 3 k } \frac { 2 } { ( 3 x - k ) } \mathrm { d } x\) is independent of \(k\),
2. show that \(\int _ { k } ^ { 2 k } \frac { 2 } { ( 2 x - k ) ^ { 2 } } \mathrm {~d} x\) is inversely proportional to \(k\).