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How to start with integral

  • Thread starter dirk_mec1
  • Start date
759
13
1. Homework Statement

Evaluate:

[tex]

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

[/tex]


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?
 
327
1
Re: integral

make two cases. One for the positive and the other for the negative
 
759
13
Re: integral

How do I know where it becomes negative?
 
327
1
Re: integral

1) all positive terms

2) bring out the negative outside of the integral.
 

Dick

Science Advisor
Homework Helper
26,258
618
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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