The diagram shows the curve \(y = xe^{-\frac{1}{4}x^2}\), for \(x \geq 0\), and its maximum point \(M\).

(a) Find the exact coordinates of \(M\).

(b) Using the substitution \(x = \sqrt{u}\), or otherwise, find by integration the exact area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = 3\).