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The diagram shows the curve \(y = ( 3 - x ) \mathrm { e } ^ { - 2 x }\) and its minimum point \(M\). The curve intersects the \(x\)-axis at \(A\) and the \(y\)-axis at \(B\).
- Calculate the \(x\)-coordinate of \(M\).
- Find the area of the region bounded by \(O A , O B\) and the curve, giving your answer in terms of e.