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Complicated double integral

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data
    I've got to calculate:

    [tex]\displaystyle\int_0^1\displaystyle\int_0^x \sqrt{4x^2-y^2} dy dx[/tex]


    2. Relevant equations



    3. The attempt at a solution

    I've tried the change of variable:
    [tex] \displaystyle t=4{{x}^{2}}-{{y}^{2}}[/tex] but it doesn't get better. I've also tried polar coordinates but it is not convinient either. Do you know a convenient change? I've been trying to figure it out for a long time.

    ** I also tried changing the order of integration but no results.


    Thanks!
     
  2. jcsd
  3. Oct 28, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    The y-integral (for any fixed value of x) is of the form
    [tex] \int \sqrt{a^2 - y^2} \, dy, [/tex]
    where it happens that a = 2x. This is a standard integral that you must surely have seen before; if not, do a change of variables using a trigonometric substitution.

    RGV
     
    Last edited: Oct 28, 2012
  4. Oct 28, 2012 #3
    Thanks! I'll try!
     
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