Given the curve \[y = \cos x - \sin x +2\] find in terms of \(a\) an expression for the area \(A\) enclosed between the axes, the ordinate \(a \; (> 0)\) and this curve. Verify that when \(a = 1.5\), \(A = 3.07\) approximately.

It is required to find the value of \(a\) for which \(A = 3\). Taking \(1.5\) as a first approximation to \(a\), find a second approximation, giving three significant figures in your answer.