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Let S1: 4y = x² (a parabola), S2: y = x/2 (a line), and S3: y² = 4x (another parabola). For x >= 2, find the area of the region bounded by these three curves.

1. 27
2. 15
3. 22/3
4. 49/3

Correct answer: 49/3

Solution

For x >= 2, the region is bounded between S3 (y²=4x, upper branch y=2*sqrt(x)) and S1 (y=x²/4) with S2 (y=x/2) as a boundary. Setting up and evaluating the integrals from x=2 to x=4 between the relevant curves gives area = 49/3.

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