Double Integrals: Evaluate I for Domain D

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Homework Help Overview

The discussion revolves around evaluating a double integral of the form I=dxdy/(x^2+y^2)^(1/2) over a specified domain D defined by the inequality 1<=x^2+y^2<=4. Participants are exploring the appropriate limits for the integral in the context of this domain.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are discussing the limits of integration for the double integral, with one suggesting the use of polar coordinates as a potential approach. There is also a mention of considering the graph of the function to determine the limits for x based on a fixed value of y.

Discussion Status

Some guidance has been offered regarding the limits of integration, with one participant indicating that one of the limits for y could be from -2 to 2. The conversation is ongoing, with participants exploring different methods and interpretations without reaching a consensus.

Contextual Notes

There is an implied need to consider the geometric representation of the domain defined by the inequality, as well as the potential transition to polar coordinates, which may affect the limits of integration.

splelvis
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to evaluate the integral:

I=dxdy/(x^2+y^2)^(1/2)


over domain D:
given by 1<=x^2+y^2<=4.

what should i take the limits to integral?
dx and dy
 
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Welcome to PF!

Hi splelvis! Welcome to PF! :smile:

(have a square-root: √ and try using the X2 tag just above the Reply box :wink:)
splelvis said:
… over domain D:
given by 1<=x^2+y^2<=4.

what should i take the limits to integral?
dx and dy

One of the limits will be -2 to 2 … let's say for y.

Then just look at the graph …

for a fixed value of y, what does x go from and to? :smile:
 
thank you i got that
 
Hello,
I think polar coordinates is a good choice for this one. :)
 

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