#### dirk_mec1

1. Homework Statement

Evaluate:

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

2. Homework 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?

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#### tnutty

Re: integral

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

#### dirk_mec1

Re: integral

How do I know where it becomes negative?

#### tnutty

Re: integral

1) all positive terms

2) bring out the negative outside of the integral.

#### Dick

Homework Helper
Re: integral

How do I know where it becomes negative?
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|).

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