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. :-)
I just don't ever remember seeing it done before (and I'm old enough to
remember when we didn't have calculators, much less computer algebra systems).
Not really trying to start a thread here on how much, if any, techniques of
integration we should teach. Just curious as to the specific question I asked.
Thanx!!
Bret Taylor Lake-Sumter Community College Leesburg, FL
"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes, most of all, is what the teachers are themselves."
John Wooden
John 3 : 3^3 + 3
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