Final answer:
To find the volume of the solid obtained by rotating the region bounded by the curves y = ln(7x), y = 1, y = 6, x = 0 about the y-axis, we will use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the curves y = ln(7x), y = 1, y = 6, x = 0 about the y-axis, we will use the method of cylindrical shells.
We will integrate the volume of each shell, which is the product of the circumference and the height, with respect to y from y = 1 to y = 6.
The volume of the solid is given by the integral V = 2π ∫[1,6] x ln(7x) dy.