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\includegraphics[max width=\textwidth, alt={}, center]{efa44efb-9350-4d54-b5e1-4f722781a5f3-3_366_764_1914_687} The diagram shows the curve \(y = \frac { x ^ { 2 } } { 1 + x ^ { 3 } }\) for \(x \geqslant 0\), and its maximum point \(M\). The shaded region \(R\) is enclosed by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = p\).

1. Find the exact value of the \(x\)-coordinate of \(M\).
2. Calculate the value of \(p\) for which the area of \(R\) is equal to 1 . Give your answer correct to 3 significant figures.