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Evaluate the triple integral (with spherical coordinates)

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Firstly sorry for my bad english,i have a one question for you(İ try it but i didn't solve it )

    2. Relevant equations



    3. The attempt at a solution
    i know problem will be solved spherical coordinates but i dont know how i get angles (interval) theta and fi ?
    [tex]\int_{0}^{\infty}\int_{0}^{\infty}\int_{0}^{\infty}e^{-\sqrt{x^2+y^2+z^2}}\,dxdydz[/tex]

    Mod note: Fixed LaTeX. Read what tiny-tim said below.
     
    Last edited by a moderator: May 14, 2012
  2. jcsd
  3. May 14, 2012 #2

    HallsofIvy

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    Re: evaluate the tripple integral (with spherical coordinates)

    You get the angles by thinking about what the spherical coordinate variables mean. [itex]\phi[/itex] is the angle from the positive z-axis to the negative x-axis and, to cover all space, would normally go from [itex]0[/itex] to [itex]\pi[/itex]. Since you want z to stay positive, you want [itex]\phi[/itex] to go from [itex]0[/itex] to [itex]\pi/2[/itex]. [itex]\theta[/itex] goes around a complete circle in the xy-plane in going from [itex]0[/itex] to [itex]2\pi[/itex]. Since the first quadrant is 1/4 of that, [itex]\theta[/itex] goes from [itex]0[/itex] to [itex]\pi/2[/itex]. Finally, there is no upper limit on the distance from the origin to any point in the first octant so [itex]\rho[/itex] goes from [itex]0[/itex] to [itex]\infty[/itex].
     
  4. May 14, 2012 #3

    tiny-tim

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    welcome to pf!

    hi melihaltintas! welcome to pf! :smile:

    don't try to put forum tags inside latex! :wink: …​
     
  5. May 15, 2012 #4
    thanks a lot :)
     
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