Let R be the region bounded by the graph of f(x) = cx(1 - x) and the

Question:

Let R be the region bounded by the graph of f(x) = cx(1 - x) and the x-axis on [0, 1]. Find the positive value of c such that the volume of the solid generated by revolving R about the x-axis equals the volume of the solid generated by revolving R about the y-axis.

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