Question 7 - A-Level Maths

Exam Board	OCR
Module	FP2 (Further Pure Mathematics 2)
Year	2007
Session	January
Topic	Integration with Partial Fractions

Express $\frac { 1 - t ^ { 2 } } { t ^ { 2 } \left( 1 + t ^ { 2 } \right) }$ in partial fractions.
Use the substitution $t = \tan \frac { 1 } { 2 } x$ to show that $$\int _ { \frac { 1 } { 3 } \pi } ^ { \frac { 1 } { 2 } \pi } \frac { \cos x } { 1 - \cos x } \mathrm {~d} x = \sqrt { 3 } - 1 - \frac { 1 } { 6 } \pi$$