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

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The discussion revolves around solving a double integration problem involving unknown variables, specifically the challenge of expressing x and y in terms of u. Participants suggest that the choice of substitution for u may be inappropriate and recommend using polar coordinates to simplify the integration process. The importance of understanding the geometric region of integration is emphasized, as well as the need to visualize the problem through diagrams. Ultimately, the conversation leads to the realization that switching to polar coordinates can significantly ease the integration task. The thread concludes with a participant expressing satisfaction upon finding the solution after considering these suggestions.
  • #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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