Final answer:
The volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis is π/3.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis, we can use the shell method.
The shell method is a technique used to find the volume of a solid of revolution, which is a three-dimensional solid that is formed by revolving a two-dimensional region around an axis.
First, let’s review the equations of the region:
y = 1/x^2
y = 0
The first equation defines the boundary of the region in the xy-plane, and the second equation defines the top of the region.
To revolve this region about the y-axis, we need to find the volume of the solid that is formed by rotating the region about the y-axis. To do this, we will use the shell method, which involves integrating the area of the region with respect to the height of the solid.
The height of the solid is given by the equation:
h(x) = 1/x^2
So, the volume of the solid is:
V = ∫[0,1] πh(x) dx
= ∫[0,1] π(1/x^2) dx
= ∫[0,1] πx dx
= π/3
Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis is π/3.
Complete question:
use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y = 1/x^2 , y = 0,