9709 P3 - Nov 2004 - Q7
1763
The diagram shows the curve \(y = x^2 e^{-\frac{1}{2}x}\).
(i) Find the \(x\)-coordinate of \(M\), the maximum point of the curve.
(ii) Find the area of the shaded region enclosed by the curve, the \(x\)-axis and the line \(x = 1\), giving your answer in terms of \(e\).
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