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Find the volume of the solid of revolution generated by revolving the region in the first quadrant bounded by the x-axis and the graph of

y = 2x − x^2 about the following.

a. the x axis
b. the y axis
c. the line x = 3
d. the y = 1

this is just like the other one. The curve is even almost identical.

see the other post and follow the steps there.
Post your work if you get stuck.

Did you know?

Did you know that you can find the volume of the solid of revolution by revolving a region in the first quadrant bounded by the x-axis and the graph of y = 2x − x^2? a. By revolving it about the x-axis, you can calculate the volume using the disk method, integrating from 0 to 2. b. By revolving it about the y-axis, you can use the shell method to find the volume, integrating from 0 to 2. c. If you revolve it about the line x = 3, you can still use the disk method, but you need to adjust the limits of integration accordingly. d. Revolving it about the line y = 1 requires a different approach, known as the washer method. You will need to subtract the volume of the hollow region from the total volume to obtain the correct answer.