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Change of varibles in integrals (More than 1 question)

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data
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    2. Relevant equations



    3. The attempt at a solution
    Why I can't integrate[itex]\theta[/itex] from 0 to 2[itex]\pi?[/itex] Then integrate [itex]\varphi[/itex] from 0 to [itex]\pi[/itex]. It seems it can also generate a sphere.

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  2. jcsd
  3. Jul 17, 2011 #2
    1. The problem statement, all variables and given/known data
    I have questions on d and e

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    2. Relevant equations



    3. The attempt at a solution
    I don't know how to integrate these functions

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  4. Jul 18, 2011 #3

    SammyS

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    For 0 < θ < π sin θ is positive, for π < θ < 2π sin θ is negative.
     
  5. Jul 18, 2011 #4

    SammyS

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    For (d) : You have the wrong limits for the θ integration.

    Also, the density is given by ρ = M π a2, where M is the mass of the circular lamina and assumes that ρ is the mass per unit area.

    For (e): Your integral has both r & θ in it.

    I suggest using r = 2a cos (θ) to find dr/dθ . What are the limits of θ for this integral ?
     
    Last edited: Jul 18, 2011
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