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Double integral on triangle using polar coordinates

  1. May 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Let R be the triangle defined by -xtanα≤y≤xtanα and x≤1 where α is an acute angle sketch the triangle and calculate
    ∫∫R (x2+y2)dA using polar coordinates
    hint: the substitution u=tanθ may help you evaluate the integral

    2. Relevant equations


    3. The attempt at a solution
    so the triangle has points (0,0) (1, xtanα) (1, -xtanα)
    and r=1/cosα=secα
    and im stuck from here i dont know how to find the θ value of the polar coordinate
     
  2. jcsd
  3. May 21, 2015 #2

    Orodruin

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    The polar angle does not have one value. Like the radial coordinate r, it is an integration variable and you must integrate over it. The question you need to answer first is: What is the integral you need to solve and what are the integration boundaries?
     
  4. May 21, 2015 #3
    i got ∫∫R r3drdθ i get that the boundary for r is 0 to secα but im stuck after this...
    i get that the polar angle is supposed to be multiple values (i.e. in a general form like θ or α) but i seriously have no clue on how to approach this further

    from the original set of data i get ∫01-xtanαxtanαx2+y2dA
     
    Last edited: May 21, 2015
  5. May 21, 2015 #4

    Orodruin

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    This is wrong. I suggest you draw the triangle on a piece of paper and try to figure out which limits your integration variables have. Think about what the angles ##\alpha## and ##\theta## represent.
     
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