Question

Disk Method: The bounded region formed by y=x^2, x = 3, and the x-axis is rotated about the line x = 3. Find the volume of the solid.

Answer 1

I believe this is a dy problem

Answer 2

limits are 0 to 9 correct?

Answer 3

yes

Answer 4

\[\pi \int\limits_{0}^{9}\left[ \sqrt{y}-3 \right]^2 dy\]

Answer 5

did I set it up correctly?

Answer 6

-9pi I believe is the solution

Answer 7

volumue can't be negative

Answer 8

what is the radius?

Answer 9

I dropped off the second power, but you are correct

Answer 10

ok I got 42.4115 I just need to integrate it by hand

Answer 11

your set up is correct. Technically it should be

V = pi (3 - sqrt(y))^2 dy, from 0 to 9
but since the difference is squared, the answer will still come out positive

Answer 12

Is it right - left or left - right?

Answer 13

I have my functions switched above

Answer 14

I believe it is right - left. I guess I still don't know my right from my left (my mistake)

Answer 15

yeah, right - left

Answer 16

no wonder I washed out of the military. haha

Answer 17

:D

Answer 18

13.5 pi or 42.411 got it Thanks