Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Change of varibles in integrals (More than 1 question)

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=37253&stc=1&d=1310913793.jpg


    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.

    attachment.php?attachmentid=37254&stc=1&d=1310913793.jpg
     

    Attached Files:

    • 3.jpg
      3.jpg
      File size:
      27.4 KB
      Views:
      162
    • 1.jpg
      1.jpg
      File size:
      36.9 KB
      Views:
      205
  2. jcsd
  3. Jul 17, 2011 #2
    1. The problem statement, all variables and given/known data
    I have questions on d and e

    attachment.php?attachmentid=37255&stc=1&d=1310914074.jpg


    2. Relevant equations



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

    attachment.php?attachmentid=37256&stc=1&d=1310914074.jpg

    attachment.php?attachmentid=37257&stc=1&d=1310914074.jpg
     

    Attached Files:

    • 4.jpg
      4.jpg
      File size:
      48.3 KB
      Views:
      160
    • 5.jpg
      5.jpg
      File size:
      35.3 KB
      Views:
      160
    • 6.jpg
      6.jpg
      File size:
      16.4 KB
      Views:
      152
  4. Jul 18, 2011 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

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

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook