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Integrate cosy/sqrt(a-y).dy

  1. Dec 29, 2011 #1

    sharks

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    The problem statement, all variables and given/known data
    Find
    [tex]\int\frac{\cos y}{\sqrt(a-y)}\,dy[/tex]

    The attempt at a solution
    Let U = cos y and dV = [tex]\frac{1}{\sqrt(a-y)}[/tex]

    I get: cosy.-2√(a-y) - 2∫√(a-y).siny.dy

    So, again, i use partial integration:
    Let U = siny and let dV = [-2(a-y)^(3/2)]/3

    I get: siny.[-2(a-y)^(3/2)]/3 + (2/3)∫[(a-y)^(3/2)].cosy.dy

    But the cycle is endless. I need to get the answer 2siny.
     
  2. jcsd
  3. Dec 29, 2011 #2

    HallsofIvy

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    No, you don't. "2 sin(y)" can't possibly be correct because the derivative of 2 sin y is 2 cos y, not "[itex]cos(y)/\sqrt{a- y}[/itex]".
     
  4. Dec 29, 2011 #3

    sharks

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    You are correct. My mistake. I solved it.
     
  5. Dec 30, 2011 #4

    LCKurtz

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    Not with any "elementary" functions; I don't think so.
     
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