`xy = 1, x = 0, y = 1, y = 3` Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by...

The shell has the radius y, the cricumference is `2pi*y` and the height is `1/y` , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

`V = 2pi*int_1^3 y*(1/y) dy`

Reducing like terms yields:

`V = 2pi*int_1^3 dy`

`V = 2pi*y|_1^3`

`V = 2pi*(3-1)`

`V = 4pi`

Hence, evaluating the volume, using the method of cylindrical shells, yields `V = 4pi.`

The shell has the radius y, the cricumference is `2pi*y` and the height is `1/y` , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

`V = 2pi*int_1^3 y*(1/y) dy`

Reducing like terms yields:

`V = 2pi*int_1^3 dy`

`V = 2pi*y|_1^3`

`V = 2pi*(3-1)`

`V = 4pi`

Hence, evaluating the volume, using the method of cylindrical shells, yields `V = 4pi.`