$\int_{0}^{2008}x|\sin\pi x| dx$ Evaluate: 
$$\int_{0}^{2008}x|\sin\pi x| dx$$
That modulus sign is causing problems. How do I handle it?
I am trying integration by parts
I have even evaluated: $\int_0^1 {|\sin \pi x|}= \frac 2 \pi$. Not sure how to utilise it in the problem. 
I just need help with the modulus part. 

Not sure how to bring graphs into answers, but here is a link to your function.
http://www.wolframalpha.com/input/?i=graph+%7Csin(pix)%7C
As you can see, the period is $1$, i.e. if
$f(x)=|\sin(\pi x)|$ then $f([0,1])=f([1,2])$.
So $\int_0^{2008}f(x) dx = 2008\int_0^1 f(x) dx$
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