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The diagram shows the curve \(y = x ^ { 2 } \mathrm { e } ^ { 2 - x }\) and its maximum point \(M\).
- Show that the \(x\)-coordinate of \(M\) is 2 .
- Find the exact value of \(\int _ { 0 } ^ { 2 } x ^ { 2 } \mathrm { e } ^ { 2 - x } \mathrm {~d} x\).