Finding the Mean Number of Screams on a Roller Coaster Ride

[the7joker7]

Homework Statement

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.

The answer: 4.71238898038

Homework Equations

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

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?

 

[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?

 

[the7joker7]

It's not given.

 

[tiny-tim]

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

Does that help?

 

[foxjwill]

It's not given.

which?

edit:

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

 

[the7joker7]

The units, and length.

 

[foxjwill]

The units, and length.

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