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Compute the area (in square units) of the region enclosed between the curves y = x*(x - 3)² and the line y = x.

1. 28
2. 32
3. 4
4. 8

Correct answer: 8

Solution

The curves meet at x = 0, 2, 4. Integrating |x(x-3)² - x| over these intervals gives a total enclosed area of 8 square units.

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