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CAl 3

  1. Nov 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Let f(x,y,z) be a continuous function. To rewrite f(x,y,z) as a function of spherical coordinates, the conversion x-rcos([tex]\theta[/tex]), y=rsin([tex]\theta[/tex]), and z=rcos([tex]\varphi[/tex]). Suppose S is a region in 3 dimensions. How would you rewrite [tex]_{\int\int\int}s[/tex] f(x,y,z)dV as the integral of a function in terms or r,[tex]\theta[/tex], and[tex]\varphi[/tex]



    Note the s by the integral should be a subscript

    2. Relevant equations
    Hint, may require a change of variable formula



    3. The attempt at a solution

    I attempted to plug in the conversion of x, y, and z, but i dont think this is what is needed. I believe it is more of a conceptual question. What should i do?, im comfortable with the integration or deriving of the stuff, but am not sure what he is actually is asking. This isnt a homework problem to turn in, but something we were supposed to look at.
     
  2. jcsd
  3. Nov 3, 2009 #2

    rock.freak667

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    Homework Helper

    Do you know of a function called the Jacobian function? Because you will need this to find out what dV changes to.


    Also I think x=rcosθsinψ y=rsinθsinψ z=rcosψ
     
  4. Nov 3, 2009 #3
    no, ive never seen jacobian's. I know the name and have heard them mentioned, but have never seen them

    It says home work, buts it on the bottom of a test review, its not something to turn in, i can post the entire test review if you dont believe me, where it says it at the top of the page

    here is a copy of the problem in case i typed it wrong
    qxo0gp.jpg
     
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