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Determine the area enclosed by the curve x² = 2 - y - y² and the y-axis.

1. -9/2
2. 9/2
3. 9
4. -9

Correct answer: 9/2

Solution

The curve x = 2 - y - y^2 crosses the y-axis (x=0) at y = -2 and y = 1. Area = integral_{-2}^{1} (2 - y - y^2) dy = [2y - y^2/2 - y^3/3]_{-2}^{1} = 7/6 + 10/3 = 9/2.

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