Question

Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line.

y =10/x²
y = 0
x = 1
x = 5
(a) the x-axis
(b) the y-axis
(c) the line y = 10

Answer 1

The question concerns finding the volume of a solid by rotating a region defined by several functions around the x-axis, y-axis, and the line y = 10 using integral calculus' disk or shell methods. Information on moments of inertia given in the references is inapplicable here.

Step-by-step explanation:

The question asks for the volume of the solid generated by revolving a region around different axes using disk or shell methods. The region is bounded by the equations y = 10/x², y = 0, x = 1, and x = 5. The revolution occurs about the x-axis, the y-axis, and the line y = 10. However, since the provided reference text discusses moments of inertia, which is a concept from physics and not directly related to finding volumes of solids via integral calculus, the reference to moments of inertia is irrelevant to solving this problem using the disk or shell method.

To calculate the volume using the disk method for the revolution around the x-axis, one would integrate πy² from x = 1 to x = 5. For the revolution about the y-axis, the shell method may be more suitable, determining the volume by integrating 2πxy over the y-values that the function spans. For the line y = 10, again the shell method would be used, taking into account the displacement from the axis of rotation.