Question 6 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2017
Session	November
Topic	Standard Integrals and Reverse Chain Rule

Find the exact value of \(\int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \sin x ( 4 \sin x + 6 \cos x ) \mathrm { d } x\).
Given that \(\int _ { 0 } ^ { a } \frac { 6 } { 3 x + 2 } \mathrm {~d} x = \ln 49\), find the value of the positive constant \(a\).