Solving a Double Integration Problem with Unknown Variables: How to Proceed?

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Homework Help Overview

The discussion revolves around a double integration problem where the original poster is struggling to express variables x and y in terms of a new variable u. The context involves evaluating an integral that appears to relate to circular geometry.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the choice of substitution for u, with some suggesting that a different variable might be more appropriate. There are inquiries about the completeness of the problem statement and the limits of integration. The original poster expresses difficulty in expressing x and y in terms of u and seeks clarification on how to proceed.

Discussion Status

There is an ongoing exploration of the problem with various participants offering hints and suggestions. Some participants have pointed out potential issues with the original poster's approach, while others have encouraged visualizing the integration limits. The discussion reflects a mix of interpretations and attempts to clarify the problem without reaching a consensus.

Contextual Notes

Participants note that the original poster's work may be unclear and that there are constraints related to the integration limits and the geometric interpretation of the region of integration. There is also mention of the need to understand the implications of changing the order of integration.

  • #31
You answer the question
BvU said:
what ##\ x\over \sqrt{x^2 + y^2} ##represents
 
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  • #32
BvU said:
You answer the question
it has no meaning , right ? the author just simply put inside the equation, right ?
 
  • #33
You think I annoy you with so many questions when there is no meaning ? What is the sine of the red angle ? What is the cosine ?
upload_2016-9-12_13-46-56.png
 
  • #34
BvU said:
You think I annoy you with so many questions when there is no meaning ? What is the sine of the red angle ? What is the cosine ?
View attachment 105794
BvU said:
You answer the question
It's cos theta, so?
 
  • #35
chetzread said:
It's cos theta, so?

What do you think?
 
  • #36
@chetzread, I believe that BvU's hint is not about merely switching the order of integration (i.e., dxdy vs. dydx), but instead, about changing to a polar integral. This problem quite a bit easier if you do it this way.
 
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  • #37
chetzread said:
It's cos theta, so?
So ? Wouldn't substituting ##\theta## as integration variable be a sensible thing to try ?
 
  • #38
BvU said:
So ? Wouldn't substituting ##\theta## as integration variable be a sensible thing to try ?
ok, i got the ans now ...I'm wondering is this a special case? I have never learned and see this before ...
 
  • #39
Humor me and tell me what you did ...
 
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  • #40
BvU said:
Humor me and tell me what you did ...
 
  • #41
You said
chetzread said:
ok, i got the ans now
could you share your working with us ?
 

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