Final answer:
To find the volume of the solid of revolution when the region Ω bounded between the curves y=3 √(x) and y=x is rotated about the x-axis, we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid of revolution when the region Ω bounded between the curves y=3 √(x) and y=x is rotated about the x-axis, we can use the method of cylindrical shells. The volume of a solid of revolution can be found by integrating the product of the height of each shell and its circumference. In this case, the height of each shell is given by the difference between the two curves, which is y=3 √(x)-x, and the circumference is 2πx. To set up the integral, we can express the volume as an integral from x=0 to x=a, where a is the x-coordinate of the point where the curves intersect. The integral is: ∫ 2πx(3 √(x)-x) dx.