Find the volume of the solid generated by revolving the shaded region about the x-axis. The curve is y equals StartFraction 15 Over StartRoot 15 x minus x squared EndRoot EndFraction ; x 1 equals 2, x 2 equals 12.

Explanation:

We are required to find the volume of the solid generated by revolving the shaded region about x-axis on the interval [a, b] = [2, 12] for the following function

To find the volume we integrate its area

where A = πr² and

So the volume becomes

Integrating yields

Evaluating the limits a = 2 and b = 12

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