Wacky change of variables for Multi integration

In summary, the conversation is about difficulties with solving problems involving multiple integrals and using change of variables. The speaker provides a link to an example problem and asks for help with solving it. They also ask for clarification on the proper transformation for another problem. The conversation ends with the speaker successfully solving both problems and thanking the other person for their help.
  • #1
Theelectricchild
260
0
Wacky change of variables for Multi integration!

Arghh I am having diffiiculty with these problems.
I am having difficulty mastering the LaTeX form--- (things like how to make a double integral etc) so

if you look at this site

http://www.math.washington.edu/~m124/Stewart5Eprobs/5ET-15problems.pdf

and look at page 1040 in the text (ch 15.9) the problem in question is number 14...

I am having a really tough time rewriting the integrand in u,v form with the given transformation. Perhaps there was a mistake in my algebra--- but what would be the way to go about doing this?

and also for number 20... would the proper transformation be u = x+y and v = x^2 - y^2 ? Or would something else work better.

Again I apologize for posting a link--- I promise I will take the time to learn LaTeX before I post--- I just have a tough time with Change Of Variables overall.

Thanks for all your help.
 
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  • #2
Oops, make that Page 1048, not 1040---
 
  • #3
haha nm i figured out 20--- its better to expand the x^2 - y^2 ... makes life good.
 
  • #4
For #14, I get the intermediate integral

[tex]2\int_R(u^2 + v^2) \frac{\partial (x,y)}{\partial (u,v)} \, dA[/tex]
where
[tex]R: \quad u^2 + v^2 = 1[/tex]

Which can then be changed into polar coordinates to be evaluated.

For #20, I'd try the substitutions u = x + y and v = x - y.

cookiemonster
 
  • #5
Wow thanks cookie I got it! The integrand turns out nicely coz the region is a simple circle--- and easily evaluated using polor coordinates!
 

1. What is a "wacky" change of variables for multi integration?

A "wacky" change of variables for multi integration refers to a non-traditional or unconventional substitution of variables in a multiple integral. It may involve using unusual functions or transformations to simplify the integral and make it easier to solve.

2. How is a "wacky" change of variables different from a regular change of variables?

A "wacky" change of variables differs from a regular change of variables in that it may not follow the traditional steps or use commonly used functions. It may also be more difficult to determine the appropriate substitution or transformation to use.

3. Are there any benefits to using a "wacky" change of variables for multi integration?

Yes, there can be benefits to using a "wacky" change of variables for multi integration. It may allow for a more efficient or simplified solution to the integral, and can also provide a different perspective on the problem and help to develop a deeper understanding of the concept.

4. How do I know when to use a "wacky" change of variables for multi integration?

Knowing when to use a "wacky" change of variables for multi integration can be challenging. It often requires experience and intuition to determine when a non-traditional approach may be beneficial. It is important to carefully consider the problem and try different substitutions or transformations to see which yields the most manageable integral.

5. Are there any drawbacks to using a "wacky" change of variables for multi integration?

While there can be benefits to using a "wacky" change of variables, there can also be drawbacks. It may be more time-consuming and difficult to determine the appropriate substitution or transformation to use. Additionally, the resulting integral may be more complex and difficult to evaluate compared to a traditional change of variables.

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