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The region enclosed between the parabolas y = a - x² and y = x² has an area of 18*sqrt(2) square units. Determine the value of the positive constant 'a'.

1. 4
2. 6
3. 9
4. 12

Correct answer: 9

Solution

The two parabolas, an upward one (y = x²) and a downward one (y = a - x²), intersect symmetrically about the y-axis. The vertical gap between them is (a - x²) - x² = a - 2x². Integrating this gap across the intersection limits gives the enclosed area, which depends only on a. Equating it to the given area yields a single value of a.

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