1. Mar 28, 2009

### dirk_mec1

1. The problem statement, all variables and given/known data

Evaluate:

$$\lim_{n\to\infty} \int_0^{\frac{\pi}{2}} x|\cos nx|\ \mathrm{d}x$$

2. Relevant equations
hint: the integral is not zero.

3. The attempt at a solution
I don't know how to start: how do I deal with the absolute sign?

2. Mar 28, 2009

### tnutty

Re: integral

make two cases. One for the positive and the other for the negative

3. Mar 28, 2009

### dirk_mec1

Re: integral

How do I know where it becomes negative?

4. Mar 28, 2009

### tnutty

Re: integral

1) all positive terms

2) bring out the negative outside of the integral.

5. Mar 28, 2009

### Dick

Re: integral

It changes sign everywhere cos(nx) vanishes, when nx is an odd multiple of pi/2. You might find it easier to count if you do the change of variables u=nx first. Then follow tnutty's advice and add up the positive parts and negative parts separately. Try and guess the answer first. For large n you get many cosine cycles. So it ought to be the integral from 0 to pi/2 of x*(the average value of |cos|).