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\includegraphics[max width=\textwidth, alt={}, center]{c52fe7e9-0442-4b3e-b924-2e5e4b3e98f5-04_584_785_255_680}
The diagram shows the curve \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = - 4 x ^ { 3 } + 9 x ^ { 2 } + 10 x - 3\).
- Verify that the curve crosses the \(x\)-axis at ( 3,0 ) and hence state a factor of \(\mathrm { f } ( x )\).
- Express \(\mathrm { f } ( x )\) as the product of a linear factor and a quadratic factor.
- Hence find the other two points of intersection of the curve with the \(x\)-axis.
- The region enclosed by the curve and the \(x\)-axis is shaded in the diagram. Use integration to find the total area of this region.