The graph shows a sketch of part of the curve C with equation y = x(x +

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The graph shows a sketch of part of the curve C with equation y = x(x + 3)(2 − x). The curve C crosses the x-axis at the origin O and at points A and B.


a. Write down the x-coordinates of A and B.  The finite region, shown shaded, is bounded by the curve C and the x-axis.


b. Use integration to find the total area of the finite shaded region.


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