Use the Method of Cylindrical Shells to Find the Volume $$y = \frac { 1 } { x \left( x ^ { 2 } + 144 \right) } , \quad y = 0 , x = 1 , x = 12 ; \text { the } y \text {-axis }$$

question 135

Essay

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
$$y = \frac { 1 } { x \left( x ^ { 2 } + 144 \right) } , \quad y = 0 , x = 1 , x = 12 ; \text { the } y \text {-axis }$$

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