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Definate integral help

  1. Feb 6, 2005 #1
    in all seriousness because of the hurricanes in florida i did not get to learn about finding integrals in the Y perspective. given that this is my question.

    let R be the region in the first quadrant bounded by x=0,y=1,y=2, and
    y= 4e^(-x^2). to my knowledge the integral needs to be set up so that we change perspectives make the y axis the x axis and the x axis the y axis. so we cut the graph with an arbitray "horizantol" line. so this gives us the integral from x=1 to x=2 (former y values). here is my problem the first horizontal line that Y touches is Y=0 (former x value) and y = 4e^(-x^2). now since we changed our coordinate system don't we need to change the exponeltial function thus x=4e^(-y^2) and solve for Y?
     
  2. jcsd
  3. Feb 6, 2005 #2

    dextercioby

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    Not really,u need to find
    [tex] y^{-1}(x) [/tex]

    Daniel.

    If you don't like it,then how about
    [tex] y(x_{1})=1 [/tex]

    [tex] y(x_{2})=2 [/tex]

    The solutions will be your new integration limits...
     
  4. Feb 6, 2005 #3
    isn't [tex] y^{-1}(x) [/tex] the same thing as x=4e^(-y^2) and solve for Y? is this not the inverse of Y also
     
  5. Feb 6, 2005 #4

    dextercioby

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    Find x=x(y) and integrate between y_{1}=1 & y_{2}=2...

    Daniel.
     
  6. Feb 6, 2005 #5
    so is y=sqrt(ln4-lnx) my function to integrate?
     
  7. Feb 6, 2005 #6

    dextercioby

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    Yes,it looks ugly,since it involves the function "erf"... :yuck:

    Daniel.

    P.S.Really ugly indeed...
     
  8. Feb 6, 2005 #7
    man that looks so ugly and WRONG i hope this is correct. so what i have now is this
    integral from 1 to 2 of sqrt(ln4-lnx). this is the area you say
     
  9. Feb 6, 2005 #8

    dextercioby

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    Yes,try to integrate:
    [tex] \int_{1}^{2} \sqrt{\ln 4 -\ln x} \ dx [/tex]

    Daniel.
     
  10. Feb 6, 2005 #9
    thank you. i'll try that
     
  11. Feb 6, 2005 #10
    i used my calculator and got an are of approx 0.995121: this seems very small
     
  12. Feb 6, 2005 #11

    dextercioby

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    I would't know what the final outcome would be,simply because it's pretty difficult to get...
    Try to do it by hand,though.

    Daniel.
     
  13. Feb 7, 2005 #12
    i got it, the above is the correct solution. thank you
     
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