The region R is bounded by the x-axis, x = 2, and y = x^2. What expression represents the volume of the solid formed by revolving R around the line x = 2?

Question

It seems that I'm not allowed to post images, so I will try to type out my answer:
∫[0, 4] π * (2-√y)^2 dy

Can anyone confirm that this is correct? I used what I believe is called the "disc" method. I'm not very familiar with the "shell" method (was not included in our class) so I would love to know if anyone agrees with my answer.

Answer 1

I agree with you and I have an answer.
Let me know what you got, so I can check it

Answer 2

Hi! My question only wants the answer in the form of an integral, so I think I'm going to put down ∫[0, 4] π * (2-√y)^2 dy. In the form of an actual number, I believe that this is 8pi/3?

Answer 3

I agree with that numerical answer.