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Cottontails

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Suppose A is rotated around the vertical line x=7 to form a solid revolution S.

So, using the shell method, I was able to find the indefinite integral used.

I found the shell radius to be (7-x) and the shell height to be (9-x^2)

Therefore, the volume is 2∏∫(7-x)(9-x^2)dx = 2∏∫(63-9x-7x^2+x^3)Δx

However, I am just unsure for what the interval should be. For whether it should be [-3,3] or [0,7]. So, which one is it?

I also tried using the disc method, with π ∫ [7² - (9 - y)] dy from 0 to 9 and got the answer 801∏/2. Is that right?

Any help is appreciated. Thanks.