Question 6 - A-Level Maths

Exam Board	AQA
Module	FP2 (Further Pure Mathematics 2)
Year	2010
Session	January
Topic	Integration using inverse trig and hyperbolic functions

Show that the substitution $t = \tan \theta$ transforms the integral $$\int \frac { \mathrm { d } \theta } { 9 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta }$$ into $$\int \frac { \mathrm { d } t } { 9 + t ^ { 2 } }$$
Hence show that $$\int _ { 0 } ^ { \frac { \pi } { 3 } } \frac { d \theta } { 9 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta } = \frac { \pi } { 18 }$$