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8-102.

The graph at right shows . Write an integral that will compute the volume of the solid when this region is rotated about: Homework Help ✎

  1. The -axis.

    Vertical rectangles.

  2. The -axis.

    Horizontal rectangles would be very difficult (because the inverse of is NOT a function). Use the Shell Method.

  3. The line .

    Recall that each cylindrical shell is a prism with dimensions: .
    represents the (radius) in the circumference part of the formula: . (Why?)

    By shells: 

  4. The line .

    Vertical rectangles with a hole in the center.