What Are the Steps for Using Change of Variables to Find Bounded Regions?

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Homework Help Overview

The discussion revolves around using change of variables to identify a region bounded by the curves y = x, y = 2x, xy = 1, and xy = 2. The original poster expresses uncertainty about how to introduce new variables for the transformation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss potential choices for new variables u and v, with suggestions to set one variable equal to xy to achieve constant limits. There is also exploration of how to select u to ensure constant limits for the other bounding equations.

Discussion Status

Some guidance has been offered regarding the selection of variables and the implications for the limits of integration. The original poster acknowledges confusion stemming from a missed example in class, indicating a productive exchange of ideas without a clear consensus yet.

Contextual Notes

The original poster references difficulty in understanding the initial steps of the problem, despite feeling more confident about subsequent steps. There is an indication of reliance on textbook examples that may not align with their current understanding.

mattbonner
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Homework Statement


using change of variables, find the region bounded by
y = x, y = 2x, xy = 1, xy=2


Homework Equations





The Attempt at a Solution


i know i have to introduce the variables u, v
the problem is i don't understand how to introduce them
i tried read the textbook but the examples all introduce the new variables for you

i think i understand the steps that follow, I am just stuck at the beginning
 
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Well, you would like your uv integral to have constant limits if possible. You have xy=1 and xy=2 so that certainly suggests setting u or v = xy. If you use v, then v will go from 1 to 2.

Now can you see how to choose u so that y = x and y = 2x give you constant limits for u?
 
i guess y/x?
that'll give me 1 to 2 as well?
 
Good guess. I hope it wasn't a pure guess. You don't have to ask about the limits. Look at the equations. And plot your uv region.
 
i vaguely remembered a similar example the prof did, i missed how he had chosen u and v, which resulted in my confusion

thank you so much for the help!
 

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