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\includegraphics[max width=\textwidth, alt={}, center]{49e137bf-42cc-41af-b5d9-85301d4699b8-12_883_1703_267_182}
The diagram shows the curves with equations \(y = x ^ { 3 } - 3 x + 3\) and \(y = 2 x ^ { 3 } - 4 x ^ { 2 } + 3\).
- Find the \(x\)-coordinates of the points of intersection of the curves.
- Find the area of the shaded region.