Final answer:
To find the volume of the solid formed by rotating the region enclosed by the curves y = 11x, y = 3x, and x = 0 about the y-axis, use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid formed by rotating the region enclosed by the curves y = 11x, y = 3x, and x = 0 about the y-axis, we need to use the method of cylindrical shells.
The volume of the solid can be found by integrating the volume of each cylindrical shell from 0 to the x-coordinate of the intersection point of the curves.
The radius of each cylindrical shell is the x-coordinate, and the height is the difference between the y-values of the curves. After integrating, the volume can be expressed as V = ∫(2πx(11x-3x))dx.