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For x > 1, find the total area of the region enclosed by the three curves y = -x² + 6x - 5, y = -x² + 4x - 3, and y = 3x - 15.

1. 73
2. 13/6
3. 73/6
4. none of these

Correct answer: 73/6

Solution

The two parabolas meet at x = 1 (for x > 1) and diverge, while the line intersects the lower parabola at x = 4 and the upper parabola at x = 5. Splitting the enclosed region at x = 4 and integrating gives a total area of 73/6.

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