Integral problem
- To: mathgroup at smc.vnet.net
- Subject: [mg16425] Integral problem
- From: "Nicolas B.E. Sawyer" <nbes at eee.nott.ac.uk>
- Date: Sat, 13 Mar 1999 02:21:41 -0500
- Organization: University of Nottingham
- Sender: owner-wri-mathgroup at wolfram.com
If
f[x_]:=x/E^(a*Sqrt[x^2 + b^2]),
given that
1) theInt=Simplify[Integrate[f[x], x]] =
2 2
1 + a Sqrt[b + x ]
-(-------------------)
2 2
2 a Sqrt[b + x ]
a E
2) PowerExpand[Limit[theInt, x -> 0]] =
1 + a b
-(-------)
2 a b
a E
3) Limit[theInt, x -> Infinity] = ComplexInfinity
and 4) (with a positive and real) Limit[theInt/.a->9, x -> Infinity] = 0
Why can't I integrate f[x] between 0 and infinity as follows?
In[26]:=
Integrate[f[x], {x,
0,Infinity},Assumptions->{Re[a]>0,Im[a]==0,Re[b]>0,Im[b]==0}]
Out[26]=
x
Integrate[----------------, {x, 0, \[Infinity]},
2 2
a Sqrt[b + x ]
E
Assumptions -> {Re[a] > 0, Im[a] == 0, Re[b] > 0, Im[b] == 0}]
--
Nicolas B.E. Sawyer
Department of Electrical and Electronic Engineering,
University of Nottingham,
University Park,
Nottingham,
NG7 2RD.
Tel: +44 115 9515151 ext 12028
Fax: +44 115 9515616
E-mail: nbes at eee.nottingham.ac.uk