$\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.

Printable View

- Dec 21st 2013, 06:43 AMlawochekelriemann 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 AMromsekRe: riemann stieltjes integral!
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 PMPlatoRe: riemann stieltjes integral!
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 AMromsekRe: 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 PMlawochekelRe: riemann stieltjes integral!
thanks guys.