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Spherical coordinates triple integral

  1. Nov 20, 2005 #1

    Please can someone help me with this problem:

    find the triple integral over T( using spherical coordinate)

    T: 0<=x<=1
    0<= y<=sqrt(1-x^2)
    sqrt(x^2+y^2)<= z <= sqrt(2-(X^2+y^2))

    please help me just to find the boundaries of the integrals.
    I tried but I did not find the solution of the textbook. ( because I set the wrong triple integral) I also tried to draw a picture but ...nothing

    Thank you
  2. jcsd
  3. Nov 21, 2005 #2
    Use the relations between Cartesian (x,y,z) and spherical coordinates ([itex]r,\theta,\phi[/tex]) to substitute for x, y and z:


    where phi is the angle between a vector and the z-axis. theta is the angle between the projection on the x,y plane ad the x-axis.
  4. Nov 21, 2005 #3


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    Homework Helper

    Also don't forget your Jacobian, in this case being r²sin(phi).
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