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Help with an integral

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data

    I can't seem to figure out how to solve this integral:


    2. Relevant equations


    3. The attempt at a solution

    I tried doing integration by parts by first letting v=d[tex]\Theta[/tex] and dV=[tex]\Theta[/tex], and U=cos2(2[tex]\Theta[/tex]) and dU=-4[tex]\Theta[/tex]cos(2[tex]\Theta[/tex])sin(2[tex]\Theta[/tex])d[tex]\Theta[/tex], and then putting it into the form [tex]\int[/tex]UdV=UV-[tex]\int[/tex]VdU, but that didn't really take me anywhere. Is there another way I should try to solve this integral? This is my fourth university calc class, and the full question is double integrals with polar coordinates, so I probably learned how to solve these types of integrals somewhere down the road, I just can't seem to remember. Thanks in advance
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 22, 2010 #2


    Staff: Mentor

    Hint: cos2(t) = (cos(2t) + 1)/2
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