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Find the area enclosed between the curve a² y = x² (x + a) and the x-axis.

1. a²/3 sq. units
2. a²/4 sq. units
3. 3a²/4 sq. units
4. a²/12 sq. units

Correct answer: a²/12 sq. units

Solution

The curve cuts the x-axis at x = -a and x = 0 (double root); integrating y between these limits gives a²/12.

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