CPM Homework Banner

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

  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.

First quadrant curve labeled, f of x, starting at the point (0, comma 4), rising to about (1, comma 4.5), changing from concave down to concave up at about x = 2, turning at approximate point (3.5, comma 2.5), continuing up & right, shaded region below the curve, above x axis, right of y axis, and left of x = 5.