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Homework Help: Double Integrals

  1. Nov 4, 2004 #1
    This might be somewhat of a mundane question but I can't seem to figure it out. It has to do with the limits of integration for a double integral. The initial integral is as follows...

    1 √(1=y^2)
    ∫ ∫ 1/(1+x^2+y^2) dx dy
    0 0

    I hope the formatting on that doesn't get screwed up. Anyway, the point of the excercise is to convert this to polar and do the integral then. I can convert the equation easy enough, especially due to the x^2 and y^2 just turning into an r^2, however my question is what in the world is that one limit supposed to be? dx is first so it's like saying x = √(1=y^2)? I would imagine it is something that will convert to polar nicely since these are specially engineered excercises but I'm just not sure what to do with it with that = sign in there. There's also a second question with a similar limit y = √(2x=x^2). Sorry if this is a stupid question but I haven't encountered this notation before and it puzzles me.
     
  2. jcsd
  3. Nov 4, 2004 #2
    the best way is to draw that region to convert on the x-y plane....

    then look at it and determine the limits for dr and dtheta
     
  4. Nov 4, 2004 #3

    Kurdt

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    just think of how the polar coordinates are connected to the normal rectangular coordinates.

    x=r*cos(theta)
    y=etc
     
  5. Nov 4, 2004 #4

    Kurdt

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    actually come to think if thats the equation of a circle r will remain constant and theta will vary by 2pi. ok i'm out of practise maybe i should be quiet.
     
  6. Nov 4, 2004 #5
    It is the part of the circle in the first quadrant only :)
    the region that is
     
  7. Nov 4, 2004 #6
    Sorry, maybe I wasn't clear enough. I don't understand what the limits mean. On the y axis it's going from 0 to 1, I can see that but what about the x axis? What is meant by integrating from 0 to √(1=y^2)? I can't even figure out how to visualize this in rectangular coordinates because that "=" sign in there is confusing mean. I just don't understand the notation.
     
  8. Nov 4, 2004 #7
    =.....I am sure that is supposed to be a - lol

    EDIT: a minus, not a plus..
     
    Last edited: Nov 4, 2004
  9. Nov 4, 2004 #8

    Kurdt

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    i thought that was supposed to be a minus sign if so it comes from the equation of a circle:

    x**2+y**2=1

    can be rearranged into the upper limit of the x axis quite easily
     
  10. Nov 4, 2004 #9
    ...
    -_-;; Sorry for posting such a stupid question, it's just that he made that same typo twice and I thought it was some kind of notation... Heheh... *quietly walks away
     
  11. Nov 4, 2004 #10
    oh, sorry about that...yea, I meant a minus sign :)
     
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