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Density Function problem

  1. Feb 28, 2008 #1
    1. The problem statement, all variables and given/known data

    The density function for the number of times the riders scream on a roller coaster is given by ...

    f(x) = [tex]\frac{1}{3\pi}[/tex](1 - cos(2x)) if 0 [tex]\leq[/tex] x [tex]\leq[/tex] 3[tex]\pi[/tex]
    and 0 otherwise.

    Find the mean number of screams over the course of the ride.

    The answer: 4.71238898038

    2. Relevant equations

    None, unless integration is done by hand, in this case it doesn't have to be.

    3. The attempt at a solution

    I tried taking a several different integrals and never got close to that answer. I tried taking the integral of that function from 0 to 3[tex]\pi[/tex], I tried putting an x in front of the function, I had it read in degrees and radians, i took out the 1/3pi at the start...just anything I could think of and nothing was close to the answer. Help?
  2. jcsd
  3. Feb 28, 2008 #2
    What are the units of the density function? [tex]\frac{\mbox{screams}}{\mbox{unit length}}?[/tex]

    And over what length of track are you supposed to take it over?
    Last edited: Feb 28, 2008
  4. Feb 28, 2008 #3
    It's not given.
  5. Feb 28, 2008 #4


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    Homework Helper

    The answer, 4.71238898038, is [tex]\frac{3\pi}{2}[/tex].

    Does that help?
  6. Feb 28, 2008 #5


    Is it possible you were supposed to find the mean over the length of track from [tex]x\in \left[0,\frac{4}{3\pi}\right][/tex]?
    Last edited: Feb 28, 2008
  7. Feb 28, 2008 #6
    The units, and length.
  8. Feb 28, 2008 #7
    In that case, I think you should see if your teacher forgot something.
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