I use integration by parts to develop the reduction formula for the
integral of (sin x)^n which works for n >=2. The way I do it is not
very complicated. Check out
http://archives.math.utk.edu/visual.calculus/4/recursion.2/
and click on the first equation. You will need the Shockwave Flash
plugin to view the derivation. If you don't have it, click on the
help button on the page above and you will see a link for it.
Best,
Larry
> Has anyone ever seen or used integration by parts to derive the formula for
> THE INTEGRAL OF SINE SQUARED X ? Hope that makes sense. I'll try it this way:
>
> Integral of (sin x)^2 dx
>
> I was just playing around trying to come up with test questions on
> techniques of integration and noticed that the square of the sine of x could
> be integrated using this technique. It's rather nice, complicateed but not
> overly so - needing to use integration by parts twice and also remembering
> some trig formulas for double angles and some basic algebra. I did it in
> class today, more to remind the students that they still needed to remember
> facts from trig than to expect them to use this technique for this integral.
> Just a nice ten minute excursion into the wonderful world of calculus. :-)
>
------------------------------------------------------
Larry Husch phone:423-974-4162 fax:423-974-6576
Dept.Mathematics http://www.math.utk.edu/~husch
Univ. Tennessee Co-Director, Mathematics Archives
Knoxville, TN 37996 http://archives.math.utk.edu/
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************