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Let .

  1. Calculate the area of the region bounded by , the -axis, and .

    Before you set up an integral, sketch the graph and shade the region.

  2. If the line divides the region from part (a) into two pieces of equal area, what is the value of ?

    Solve for .

  3. Calculate the volume of the solid that is formed by rotating the region described in part (a) about the -axis.

    Use disks.

  4. If a plane perpendicular to the -axis at divides the solid in part (c) into two parts of equal volume what is the value of ?

    Refer to the hint in part (b) and follow a similar process using a generic volume formula instead of a generic area formula.