Question

determine the volume generated by revoling the region bounded by y=2x^2, y=0, x=0, and x=5 around the line x=6

Answer 1

let's plot the functions

Answer 2

I did it correctly for the one that revoled the same area around the y axis but the new line is throwing me for a loop

Answer 3

http://www.wolframalpha.com/input/?i=Plot%5B2x%5E2%2C%7Bx%2C0%2C5%7D%5D

Answer 4

Are you familar with volumes of revolution at all?

Answer 5

It looks like x=0 is extraneous.

Answer 6

yes I have identified the region in need and just cannot figure out how to change the equation all my class was told to move the revoultion line to either the x or y axis

Answer 7

Do you use the washer method or the shell method?

Answer 8

ap cal?

Answer 9

I cannot remeber the name but we set it up like this \[V=\int\limits_{a}^{b}(f(x)^2-g(x)^2)\]

Answer 10

I forgot the time by pi on the right side sorry

Answer 11

So can you first find the limits of integration (dx, I suppose), and you need pi there somewhere.

Answer 12

okay, first think of axis or rotation minus the function in parentheses squared and don't forget the pi out front. and the dy in the back....you will need to change this to x=terms of y.

Answer 13

okay but its in setting up the new graph that I stumble I cannot for some reason seem to get the values to match the way they need to

Answer 14

that plus the reflection matchs the picture I drew for Part One Part Two is to caculate it out using the method my math teacher taugh

Answer 15

*taught

Answer 16

This should get you started.

Answer 17

I know my stuff about the graph and how it looks its the new rotation line thats tnrowing me off all other questions have been about the x or y axis

Answer 18

I understand,

First think of axis of rotation minus the function.

Answer 19

the largest radius comes first.

Answer 20

so its the line of rotation minus sqrt of y/2 its furthest away and therefore the larger radius.

Answer 21

then is smaller radius, the line of rotation minus the line x=5.

Answer 22

both are squared. since this is revolved about a vertical line you will use dy

Answer 23

if this is a calculator problem, you could now enter it.....if not there is more work to do.

Answer 24

its not but i got help with the part I needed thanks

Answer 25

k