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Consider the curve C: y = x*sqrt(9 - x²) for x >= 0. Find the area of the region bounded by C and the x-axis.

1. 9 sq. units
2. 18 sq. units
3. 27 sq. units
4. 27/2 sq. units

Correct answer: 9 sq. units

Solution

Area = integral from 0 to 3 of x*sqrt(9-x²) dx; with u = 9 - x² this evaluates to 9.

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