Math Is Fun Forum

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Triple Integration

Ok, so I'm required to set up and solve an iterated triple integral so find the volume of the solid G that is enclosed by the plane z=y, the xy-plane and the parabolic cylinder y=1-x^2.

How on earth do you find these limits!  If It's possible could someone give an analytic approach opposed to a geometric one. I find that once I can do things analytically then I find it easy to learn the geometric way!  (if this makes sense at all )   

Cheers in advance all

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Triple Integration

You can actually do it in just a single integral.

z=y is the plane at 45° to the xy-plane passing through the x-axis. The intersection of the plane

with the solid is a right triangle whose base (y-length) is

and whose height (z-length) is also

since z = y. The area of this triangle is therefore

. Hence the volume of the solid is

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Last edited by JaneFairfax (2010-12-13 12:47:16)

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Re: Triple Integration

Thanks for the post Jane, I'll look into it!!
But I've managed to solve the problem with triple integrals

     

     

     

     

     

     

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Triple Integration

Hi All;

I was playing doing the integrations for fun. Actually, I am playing with a new numerical integration idea that does not work, I am thinking of using it as a random number generator...   When I changed the integrand from y to 1 in ilovealgebra's triple integral this came up.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Re: Triple Integration

Hey Bobbym, can you please elaborate on what you are doing? It sounds interesting

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Triple Integration

Hi ilovealgebra;

Not really interesting at all, just integrating for fun.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.