Speaking of being good at math, is there ever a situation in which you have to evaluate a quadruple integral?

[Random Variable]

Or can all n-tuple integrals be reduced to triple and/or double integrals?

 

[Gibson486]

I suppose it is possible if you want to measure something in more than three demensions.....

 

[Mo0o]

4 dimensions

 

[Random Variable]

Originally posted by: Mo0o
4 dimensions

Even if you wanted the "volume" of a 4-dimensional object, I don't think you would have to evaluate a quadruple integral.

 

[Mo0o]

Why dont you google it and take a look

 

[Malak]

If it involves something beyond my multiplier table, it's not worth evaluating.

 

[DaTT]

Last night I hads to do something similar











Oh, sorry, last night I drank beer and watched the hockey game.

 

[Random Variable]

Originally posted by: Mo0o
Why dont you google it and take a look

I did but I didn't find much. What I did find suggests that there is always a way to turn it into a triple or double integral, meaning that you never actually have to evaluate the quadruple integral.

Early Sunday afternoon is probably the wrong time to ask such a question.

 

[Oscar1613]

yes, it's essential for saving your life when stranded on a desert island

 

[Random Variable]

Originally posted by: Oscar1613
yes, it's essential for saving your life when stranded on a desert island

Will it help on a deserted island?

 

[Sukhoi]

What's the difference? Aren't they just nested like double and triple are?

 

[desteffy]

Yes, there is a situation for everything

 

[Random Variable]

Originally posted by: Sukhoi
What's the difference? Aren't they just nested like double and triple are?

Do you mean the difference in evaluating them? Nothing.

 

[Sukhoi]

Originally posted by: Random Variable

Originally posted by: Sukhoi
What's the difference? Aren't they just nested like double and triple are?

Do you mean the difference in evaluating them? Nothing.

Yeah. I was confused why you were asking if n-tuple integrals could be reduced to triple integrals, since essentially they have to be through the evaluation process.

 

[Random Variable]

Originally posted by: Sukhoi

Originally posted by: Random Variable

Originally posted by: Sukhoi
What's the difference? Aren't they just nested like double and triple are?

Do you mean the difference in evaluating them? Nothing.

Yeah. I was confused why you were asking if n-tuple integrals could be reduced to triple integrals, since essentially they have to be through the evaluation process.

Like if you're finding the volume of some object, performing a triple integral is not always necessary. A lot of the time a double integral will suffice (or even a single integral).

 

[DrPizza]

Originally posted by: Random Variable

Originally posted by: Sukhoi

Originally posted by: Random Variable

Originally posted by: Sukhoi
What's the difference? Aren't they just nested like double and triple are?

Do you mean the difference in evaluating them? Nothing.

Yeah. I was confused why you were asking if n-tuple integrals could be reduced to triple integrals, since essentially they have to be through the evaluation process.

Like if you're finding the volume of some object, performing a triple integral is not always necessary. A lot of the time a double integral will suffice (or even a single integral).

Agreed, but is there a proof whereby computing the hyper-volume of some multidimensional object can *always* be reduced to a triple, double, or single integral?

Been too long for me; I don't know the answer.

 

[Sukhoi]

Argh I don't remember that stuff anymore. And on the subject I'm taking calc IV next semester. It's been a full 3 years since I finished calc III. This is gonna be fun.

 

[Heisenberg]

I do stuff with 4-d (time and space) integrals quite a bit. As for some theorem about always being able to reduce n-tuple integrals to lower dimension ones, I don't know. I'm guessing it would depend on how much symmetry is present in the problem.

 

[Random Variable]

Originally posted by: Sukhoi
Argh I don't remember that stuff anymore. And on the subject I'm taking calc IV next semester. It's been a full 3 years since I finished calc III. This is gonna be fun.

I'm taking calc 4 now (although they call it advanced multivariable calculus at my school). We're going so slow that we're just barely going to get to make it to surface integrals. In calc 3 we never got passed line integrals.

 

[Random Variable]

Originally posted by: Heisenberg
I do stuff with 4-d (time and space) integrals quite a bit. As for some theorem about always being able to reduce n-tuple integrals to lower dimension ones, I don't know. I'm guessing it would depend on how much symmetry is present in the problem.

When your integrating with respect to x, y, z, and t, does the order of integration matter?

 

[Sukhoi]

Originally posted by: Random Variable

Originally posted by: Sukhoi
Argh I don't remember that stuff anymore. And on the subject I'm taking calc IV next semester. It's been a full 3 years since I finished calc III. This is gonna be fun.

I'm taking calc 4 now (although they call it advanced multivariable calculus at my school). We're going so slow that we're just barely going to get to make it to surface integrals. In calc 3 we never got passed line integrals.

Wow your school is slow. In calc III here we did surface integrals, volume integrals, all that stuff. Here is the course description for calc IV. I guess we're redoing some of the stuff from calc III.

Introductory study of vector calculus and functions of several variables; topics include directional derivatives; Jacobians; change of variables in multiple integrals; maxima and minima; line and surface integrals; theorems of Gauss, Green, and Stokes; infinite series; and uniform convergence.

 

[Random Variable]

Originally posted by: Sukhoi

Originally posted by: Random Variable

Originally posted by: Sukhoi
Argh I don't remember that stuff anymore. And on the subject I'm taking calc IV next semester. It's been a full 3 years since I finished calc III. This is gonna be fun.

I'm taking calc 4 now (although they call it advanced multivariable calculus at my school). We're going so slow that we're just barely going to get to make it to surface integrals. In calc 3 we never got passed line integrals.

Wow your school is slow. In calc III here we did surface integrals, volume integrals, all that stuff. Here is the course description for calc IV. I guess we're redoing some of the stuff from calc III.

Introductory study of vector calculus and functions of several variables; topics include directional derivatives; Jacobians; change of variables in multiple integrals; maxima and minima; line and surface integrals; theorems of Gauss, Green, and Stokes; infinite series; and uniform convergence.

A volume integral is just another name for a triple integral.

So far we've covered partial differentiation, the chain rule for partial differentiation, gradients, directional derivatives, iterated partial derivatives, Taylor's theorem for many variables, maxima and minima of mutilvariable functions, lagrange mutlipliers for multivariable functions, the implicit function theorem, arc length, vector fields, divergence and curl, double integrals over rectangles, double integrals over general regions, changing the order of integration, triple integrals, substitution for multiple integrals/Jacobians. Path integrals looks like it will be the next subject, followed by line integrals, parametrized surfaces, surface area, integrals of scalar functions over surfaces, and surface integrals of vector fields. And there's no way in heck we're going to get to Green's Theorem, Stoke's Theorem, and the Divergence Theorem.

 

[hypn0tik]

Originally posted by: Random Variable

Originally posted by: Heisenberg
I do stuff with 4-d (time and space) integrals quite a bit. As for some theorem about always being able to reduce n-tuple integrals to lower dimension ones, I don't know. I'm guessing it would depend on how much symmetry is present in the problem.

When your integrating with respect to x, y, z, and t, does the order of integration matter?

No, the order of integration doesn't matter as long as the limits of integration for each variable are constant. However, if one limit depends on one of the other variables, then the order does matter.

 

[Random Variable]

Originally posted by: hypn0tik

Originally posted by: Random Variable

Originally posted by: Heisenberg
I do stuff with 4-d (time and space) integrals quite a bit. As for some theorem about always being able to reduce n-tuple integrals to lower dimension ones, I don't know. I'm guessing it would depend on how much symmetry is present in the problem.

When your integrating with respect to x, y, z, and t, does the order of integration matter?

No, the order of integration doesn't matter as long as the limits of integration for each variable are constant. However, if one limit depends on one of the other variables, then the order does matter.

I thought it might matter in this case even if the values of the limits are constants because you're integrating with respect to two different things-- distance and time.

 

[hypn0tik]

Originally posted by: Random Variable

Originally posted by: hypn0tik

Originally posted by: Random Variable

Originally posted by: Heisenberg
I do stuff with 4-d (time and space) integrals quite a bit. As for some theorem about always being able to reduce n-tuple integrals to lower dimension ones, I don't know. I'm guessing it would depend on how much symmetry is present in the problem.

When your integrating with respect to x, y, z, and t, does the order of integration matter?

No, the order of integration doesn't matter as long as the limits of integration for each variable are constant. However, if one limit depends on one of the other variables, then the order does matter.

I thought it might matter in this case even if the values of the limits are constants because you're integrating with respect to two different things-- distance and time.

Nope. Consider the triple integration you use in spherical coordinates to obtain the volume of a sphere. Try the integration in any order and you should get the same result.