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Find the area enclosed by the curve y = 2x⁴ - x², the x-axis, and the vertical lines through the two minima of the curve.

1. 7/120
2. 9/120
3. 11/120
4. 13/120

Correct answer: 7/120

Solution

y=2x^4-x^2 has minima at x=+-1/2. Between them the curve lies below the x-axis, so area = integral -1/2->1/2 |2x^4-x^2| dx = 7/120.

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