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Consider the curve x = y⁴ - 5y² + 4, which splits into two explicit branches: f:[-9/4, 4] -> [0, sqrt(5/2)], y = f(x) and g:[9/4, infinity) -> [sqrt(5/2), infinity), y = g(x). Let A1 be the area bounded by y = f(x), the line xy = 0 (the coordinate axes) as x varies from 0 to 4. Find A1.

1. 38/15
2. 36/15
3. 88/15
4. 3

Correct answer: 88/15

Solution

The bounded area equals the integral of x = y⁴ - 5y² + 4 with respect to y from 0 to 2, giving 88/15.

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