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Find the area (in square units) of the region {(x, y): y² >= 2x and x² + y² <= 4x, x >= 0, y >= 0}.
- pi/2 - 2*sqrt(2)/3
- pi - 4/3
- pi - 8/3
- pi - 4*sqrt(2)/3
Correct answer: pi - 8/3
Solution
The region is the part of the upper-half disc of radius 2 (centre (2,0)) lying outside the parabola y² = 2x; computing gives pi - 8/3.
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