Question 4 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2010
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Show that $\int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \cos 2 x \mathrm {~d} x = \frac { 1 } { 2 }$.
By using an appropriate trigonometrical identity, find the exact value of $$\int _ { \frac { 1 } { 6 } \pi } ^ { \frac { 1 } { 3 } \pi } 3 \tan ^ { 2 } x \mathrm {~d} x$$