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Find the area enclosed between the parabolas x² = y/4 and x² = 9y and the line y = 2.
- 10*sqrt(2)
- 20*sqrt(2)
- 10*sqrt(2)/3
- 20*sqrt(2)/3
Correct answer: 20*sqrt(2)/3
Solution
From x² = 9y, x = 3*sqrt(y); from x² = y/4, x = sqrt(y)/2. Area = 2*integral₀² (3sqrt(y) - sqrt(y)/2) dy = 20*sqrt(2)/3.
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