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\includegraphics[max width=\textwidth, alt={}, center]{9e129863-5994-4e17-81f8-e139515998d1-3_666_956_1231_593}
The diagram shows the curve \(y = x ^ { 2 } \ln x\) and its minimum point \(M\).
- Find the exact values of the coordinates of \(M\).
- Find the exact value of the area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = \mathrm { e }\).