Density Function problem

1. Feb 28, 2008

the7joker7

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) = $$\frac{1}{3\pi}$$(1 - cos(2x)) if 0 $$\leq$$ x $$\leq$$ 3$$\pi$$
and 0 otherwise.

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

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$$\pi$$, 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. Feb 28, 2008

foxjwill

What are the units of the density function? $$\frac{\mbox{screams}}{\mbox{unit length}}?$$

And over what length of track are you supposed to take it over?

Last edited: Feb 28, 2008
3. Feb 28, 2008

the7joker7

It's not given.

4. Feb 28, 2008

tiny-tim

The answer, 4.71238898038, is $$\frac{3\pi}{2}$$.

Does that help?

5. Feb 28, 2008

foxjwill

which?

edit:

Is it possible you were supposed to find the mean over the length of track from $$x\in \left[0,\frac{4}{3\pi}\right]$$?

Last edited: Feb 28, 2008
6. Feb 28, 2008

the7joker7

The units, and length.

7. Feb 28, 2008

foxjwill

In that case, I think you should see if your teacher forgot something.