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Compute the area of a region enclosed by two parabolas

by RoRi

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.

One comment

  1. S says:

    The lines intersect at point (3,2), and to compute the volume use the usual integration technique to subtract the smaller volume from the bigger one to arrive at the solution in the book.

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