# riemann stieltjes integral!

• Dec 21st 2013, 06:43 AM
lawochekel
riemann stieltjes integral!
$\displaystyle \int_{0}^{\frac{3\pi}{2}}cosx d(|cos2x|)$

pls can anybody help me with a book link or material that treat this sort of problem above, am having challenges with it.

thanks.
• Dec 21st 2013, 11:12 AM
romsek
Re: riemann stieltjes integral!
Quote:

Originally Posted by lawochekel
$\displaystyle \int_{0}^{\frac{3\pi}{2}}cosx d(|cos2x|)$

pls can anybody help me with a book link or material that treat this sort of problem above, am having challenges with it.

thanks.

there's no particular trick to this. You just need to observe where within the limits of integration |cos2x| changes sign and account for it.

$\displaystyle \cos 2x \geq 0$ on [0,pi/4], [3pi/4, 5pi/4]

$\displaystyle \cos 2x \leq 0$ on [pi/4, 3pi/4], [5pi/4, 6pi/4]

so split the integral up into these pieces using $\displaystyle \pm \cos 2x$ as appropriate.
• Dec 21st 2013, 02:57 PM
Plato
Re: riemann stieltjes integral!
Quote:

Originally Posted by lawochekel
$\displaystyle \int_{0}^{\frac{3\pi}{2}}cosx d(|cos2x|)$
help me with a book link or material that treat this sort of problem above, am having challenges with it.

This is a nasty problem. Look at this webpage.

On your question, I would do the integration by parts formula first.

Then use the derivative formula (just above that) on the new integral.
• Dec 22nd 2013, 12:56 AM
romsek
Re: riemann stieltjes integral!
my apologies. I assumed your formula was just mangled like so many here. Ignore my last post.
• Jan 6th 2014, 11:09 PM
lawochekel
Re: riemann stieltjes integral!
thanks guys.