Question

Double Integrals

Find the volume of the solid \(z=(x^2 + y^2)-1\) between the two plates z=0 and z=1

I'm not sure how to start. I've graphed the solid, but that hasn't helped me figure out what limits to use.

Answer 1

The limits would be the z axis change.

Answer 2

Then you rotate around y, with a floating radius of x.

Answer 3

That would be one way to do it.

Answer 4

Is that z = x^2 + y^2 - 1?

@PhoenixFire

Answer 5

Yeah, I don't know why they put the ( ) there.
it's the same as
\[z=x^2+y^2-1\]

Answer 6

It would be a shift on the z axis. You can still reduce it to a single axis problem, which was what I was thinking of.

Answer 7

@e.mccormick I'm not quite sure how you would do that.

Answer 8

Or I think you can... hehe. I have been known to be wrong!

Answer 9

@Hoa Yes! Give us some direction if you know how to do it.

Answer 10

@Hoa Please do, I am checking my statement! And I may be completely off here.

Answer 11

lol hoa dont bring real analysis into integrals confusing!

Answer 12

@Hoa I think polar coordinates might be the way to do this.

Answer 13

no, i'm still studying this

Answer 14

im just a chess player lol :D
but okay let's see...

Answer 15

polar coords okay?

Answer 16

it looks less menacing that way
\[\large z = r^2 - 1\]

Answer 17

Maybe it is a triple integral. I thought it would be double.

Answer 18

guys u still there?

Answer 19

Yup, just looking through my textbook to see if maybe it is a Triple.
But keep going with your solution

Answer 20

i dont have one. :(

Answer 21

maybe it does have to be in triple integrals...

Answer 22

No I actually do not have answers. It's part of my assignment. We haven't learned triple integrals yet, so maybe I'm getting ahead of myself.

Answer 23

Alright guys, thanks for trying. I'm going to close this question and do some research into it. I'll come back and ask again in a few days if it's not sorted.

Answer 24

i have an idea

Answer 25

how about
\[\Large \int\limits_{\theta = 0}^{2\pi}\int\limits_{r=1}^{\sqrt 2}(r^2-1) \ rdrd\theta\]

Answer 26

if r goes from 1 to square root of 2, then z would go from 0 to 1.

Answer 27

im sorry i didn't see
besides you probably deleted it

Answer 28

yes we meet lol
hi im Kevin Nguyen and you are...?

Answer 29

american, vietnamese dad

Answer 30

no i dont speak tieng viet

Answer 31

you gave one, i gave it again only wait for his reaction
are you a high school student?

Answer 32

big brother/sister lol

Answer 33

dont know what that means

Answer 34

maybe I will
you better not have cussed at me tho lol

Answer 35

No. I'm a college freshman.

Answer 36

@zugzwang That will give me the region


Right? Which isn't what we want.

This has to be a triple integral. I'll see if I understand it next week when we do triple integral.