Math Is Fun Forum

nha

Member

Registered: 2010-09-05

Posts: 43

triple integral

Hey everyone yet again, I have a really hard triple integral that I need help on.

My working:

But then to integrate with respect to y is very tricky for me, I can get it by calc but it is big and I want to know how to do it by hand.

Any help would be nice.

Thanks

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: triple integral

Could you just change the integration order to
y->x->z ?

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X'(y-Xβ)=0

nha

Member

Registered: 2010-09-05

Posts: 43

Re: triple integral

Could you just change the integration order to
y->x->z ?

I just tried that and it wont work, I get an integral that the calculator wont even do,

I think a different coordinate system needs to be used, but I still can't get it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: triple integral

Hi nha;

Why are you certain this one can be done?

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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.

nha

Member

Registered: 2010-09-05

Posts: 43

Re: triple integral

Hi nha;

Why are you certain this one can be done?

It is a textbook question.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: triple integral

Hi;

What textbook, do you remember?

---

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.

nha

Member

Registered: 2010-09-05

Posts: 43

Re: triple integral

Hi;

What textbook, do you remember?

Nah, from a while back but I wrote out the question in my book. Might have been stewarts.

EDIT: would converting to polars work?

Last edited by nha (2010-09-10 15:49:19)

nha

Member

Registered: 2010-09-05

Posts: 43

Re: triple integral

If it doesn't look like it can be solved I must have written it out wrong.

nha

Member

Registered: 2010-09-05

Posts: 43

Re: triple integral

Don't worry about it, I give up. I must have written it wrong. Sorry for wasting your time all.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: triple integral

Hi nha;

You haven't wasted my time. I have been trying with computers to answer your question just to see if it can be done. I managed to coax some answer out of them but I do not understand it.

---

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.

Zainix

Guest

Re: triple integral

In cylindrical coordinates:

x = r cos θ
y = r sen θ
z = z

x² + y² + r²
  _____
√x + y = r

Solve this:

pi    4    r/4
∫    ∫    ∫    (2z/r)  r dz dr dθ
°    °    °

all right?

Zainix

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: triple integral

Hi Zainix;

Welcome to the forum. Your idea is fine but I think your substitutions are incorrect. Your answer is  (4 / 3 ) π which is not correct for that triple integral.

---

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.

Zainix

Guest

Re: triple integral

Is the upper and lower bounds a error?