Question 4 - A-Level Maths

Exam Board	OCR
Module	FP2 (Further Pure Mathematics 2)
Year	2007
Session	June
Topic	Integration using inverse trig and hyperbolic functions

Given that $$y = x \sqrt { 1 - x ^ { 2 } } - \cos ^ { - 1 } x$$ find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in a simplified form.
Hence, or otherwise, find the exact value of $\int _ { 0 } ^ { 1 } 2 \sqrt { 1 - x ^ { 2 } } \mathrm {~d} x$.