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\includegraphics[max width=\textwidth, alt={}, center]{ce3c4a9c-bf83-4d28-96e2-ef31c3673dea-12_375_645_274_742}
The diagram shows the curve \(y = x \mathrm { e } ^ { - \frac { 1 } { 4 } x ^ { 2 } }\), for \(x \geqslant 0\), and its maximum point \(M\).
- Find the exact coordinates of \(M\).
- 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 \(x = 3\).