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Compute the area of a region enclosed by two parabolas

Consider the two parabolas with equations

    \[ y^2 = 2(x-1), \qquad \text{and} \qquad y^2 = 4(x-2). \]

These two parabolas enclose a region R.

  1. Compute the area of the region R using integration.
  2. Find the volume of the solid of revolution obtained by revolving R about the x-axis.
  3. Find the volume of the solid of revolution obtained by revolving R about the y-axis.

Incomplete.

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