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A curve passes through the point (0,1) and satisfies y = ∫ x² e^(x³) dx. If this curve is expressed as x = f(y), then f(y) equals

1. logₑ(3y-2)
2. ∛(logₑ(3y-2))
3. ∛(logₑ((3y-2)))
4. None of these

Correct answer: ∛(logₑ(3y-2))

Solution

The correct option is ∛(logₑ(3y-2)) because it correctly represents the inverse relationship derived from the original integral expression, ensuring that when y is substituted back, it satisfies the original curve's conditions.

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