Mathematics

Mathematics

Problem

The region bounded above by the graph of y=3x−x2y = 3x - x^{2} and below by the graph of y=xy = x is revolved about the horizontal line y=−2y = -2. For a value of xx in the interval where the region exists, which of the following expressions gives the distance from the axis of rotation to the farther of the two curves? a) x+2x + 2 b) 3x−x2−23x - x^{2} - 2 c) 3x−x2+23x - x^{2} + 2 d) ∣(3x−x2)−x∣\lvert(3x - x^{2}) - x\rvert

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