Find volume between parabloid and parabolic sylinder

[MeMoses]

EDIT - well its too late to change the title now, but I can spell corectly... sometimes.

Homework Statement

Find the volume of the region bounded by x = y**2 and z**2 and x = 2 - y**2

Homework Equations

Triple integrals and cylindricals

The Attempt at a Solution

I started by roughly graphing the two figures and I got stuck here for some reason. I tried cylindricals, but I figured there would be a better way. For whatever reason I can't get my head around the limits of integration for this problem. Solving the integral once I have it shouldn't be a problem, but I just need to setup the integral that's why my work here is limited. Thanks for any help

 

[tiny-tim]

Hi MeMoses!

EDIT - well its too late to change the title now, but I can spell corectly... sometimes.

I think you meant a diabolic sylinder!

I tried cylindricals, but I figured there would be a better way. For whatever reason I can't get my head around the limits of integration for this problem. Solving the integral once I have it shouldn't be a problem, but I just need to setup the integral that's why my work here is limited.

One surface is of revolution, but the other isn't, so there's no short-cuts here.

You'll have to take slices of width dx perpendicular to the x-axis, and then slice those slices either "horizontally" (with width dz) or "vertically" (with width dy), and double-integrate ​

 

[Biosyn]

Hi MeMoses! I think you meant a diabolic sylinder! One surface is of revolution, but the other isn't, so there's no short-cuts here.

You'll have to take slices of width dx perpendicular to the x-axis, and then slice those slices either "horizontally" (with width dz) or "vertically" (with width dy), and double-integrate ​

The real question is...
What's a Sylinder?

 

[LCKurtz]

EDIT - well its too late to change the title now, but I can spell corectly... sometimes.

Homework Statement

Find the volume of the region bounded by x = y**2 and z**2 and x = 2 - y**2

What does the red highlighted definition mean? There isn't an equation after the word "and".

 

[tiny-tim]

What does the red highlighted definition mean? There isn't an equation after the word "and".

Hi LCKurtz!

"and" means "+" ​

 

[LCKurtz]

Hi LCKurtz!

"and" means "+" ​

How do you know he doesn't mean $x = y^2$ and $x = z^2$?

 

[tiny-tim]

the title?

 

[LCKurtz]

Hi LCKurtz!

"and" means "+" ​

How do you know he doesn't mean $x = y^2$ and $x = z^2$?

the title?

Well, given that he obviously didn't post the problem word for word, I wouldn't make the assumption that the title is correct. Perhaps the problem is actually stated as I propose and the OP thinks that makes a paraboloid. No way of knowing until we see the correct wording one way or the other.

 

[MeMoses]

My bad, its x = y**2 + z**2 as thought

 

[MeMoses]

Would the limits
y**2+z**2 < x < 2-y**2,
-sqrt(1-(z**2)/2) < y <sqrt(1-(z**2)/2),
-sqrt(2) < z < sqrt(2)
get the correct volume?

 

[LCKurtz]

Would the limits
y**2+z**2 < x < 2-y**2,
-sqrt(1-(z**2)/2) < y <sqrt(1-(z**2)/2),
-sqrt(2) < z < sqrt(2)
get the correct volume?

Yes, those are correct.