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Find the area enclosed between the curve x*y² = 4*(2 - x) and the y-axis. The area is expressed as pi*lambda square units. Determine the value of lambda.

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

The curve x*y² = 4*(2-x) can be rewritten as x*(y² + 4) = 8, so x = 8/(y²+4). The region enclosed with the y-axis (x >= 0) has area computed by integrating x over all y, yielding 4*pi.

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