Final answer:
To find the volume of the solid generated when the region bounded above by y = 2sinx and y = 0 is revolved about the x-axis, we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid generated when the region bounded above by y = 2sinx and y = 0 is revolved about the x-axis, we can use the method of cylindrical shells. The volume of a cylindrical shell is given by dV = 2πx(height)(thickness). We need to integrate this expression over the given region.
Setting up the integral, we have:
V = ∫[from 0 to 2π] ∫[from 0 to 2sinx] 2πx dx dy
Simplifying the integral, we get:
V = 4π ∫[from 0 to π] x sinx dx
Evaluating this integral, we find the volume of the solid generated is approximately 12.5664 cubic units.