Spherical coordinates

  1. Hi,

    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. Use the relations between Cartesian (x,y,z) and spherical coordinates ([itex]r,\theta,\phi[/tex]) to substitute for x, y and z:

    [tex]x=rsin(\phi)cos(\theta)[/tex]
    [tex]y=rsin(\phi)sin(\theta)[/tex]
    [tex]z=rcos(\phi)[/tex]

    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. TD

    TD 1,021
    Homework Helper

    Also don't forget your Jacobian, in this case being rĀ²sin(phi).
     
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