Why no simplification ?
- Subject: [mg2536] Why no simplification ?
- From: crobc at epix.net (Christopher R. Carlen)
- Date: Fri, 17 Nov 1995 05:19:29 GMT
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: epix.net
- Sender: daemon at wri.com ( )
I evaluated the integral
Integrate[ Sqrt[4t^2 + 4 + t^-2], {t, 1, E} ]
by hand, which of course works out to E^2. By adding the terms over the
common denominator t^2, a perfect square trinomial results in the
numerator. Taking the square root yields just Integrate[ (2t^2 + 1)/t,
{t, 1, E} ] which is valid for t > 0 .
Now I can understand that Sqrt[ x^2 ] really can't be simplified to x,
but is really |x| . But in the case of a perfect square trinomial like
the above, which is always positive, why doesn't Mathematica recognize
this ?
Because it fails to recognize this simplification, the output is a big
mess, containing another integral. But anyone can see that this is
really quite a simple integral.
Anyone have any ideas how to get this integral to come out in a more
simple manner ?
_____________________
Christopher R. Carlen
crobc at epix.net
carlenC at cs.moravian.edu