Final answer:
To find the volume of the solid generated when the region bounded by the curves y=0, x=7, and x=21 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 by the curves y=0, x=7, and x=21 is revolved about the x-axis, we can use the method of cylindrical shells.
First, let's identify the height of each shell. Since the region is bounded by y=0, the height of each shell is equal to the value of y at a given x-coordinate. In this case, the height of the shell is 0.
Next, we need to find the radius of each shell. The radius is equal to the distance from the x-axis to the x-coordinate. So the radius of each shell is x.
Finally, we can use the formula for the volume of a cylindrical shell to find the volume of each shell and then integrate over the region of interest.
The volume of each shell is given by V = 2πrh, where r is the radius and h is the height. Substituting the values we found, V = 2πx(0) = 0.
The integral to find the total volume is ∫[7,21] 0 dx = 0.
Therefore, the volume of the solid generated is 0.