Question

Use the shell method to find the given volume of rotation. Describe the solid obtained by rotating the region bounded by y = ln(x), the x-axis, and y = 6 about the x-axis.

Answer 1

To find the volume of rotation using the shell method, you need to integrate the formula V = 2π∫(radius)(height)dx. The region bounded by y = ln(x), the x-axis, and y = 6 forms a shape that looks like a cylinder with a hole in the center.

Step-by-step explanation:

To find the volume of rotation using the shell method, you need to integrate the formula V = 2π∫(radius)(height)dx. The region bounded by y = ln(x), the x-axis, and y = 6 forms a shape that looks like a cylinder with a hole in the center.

Since we are rotating this shape about the x-axis, the radius is given by x and the height is given by (6 - ln(x)).

Therefore, the volume of rotation is given by V = 2π∫x(6 - ln(x))dx.