Re: Integrate[ ] returns If[ ] function; how to say it's True?
- To: mathgroup at smc.vnet.net
- Subject: [mg9397] Re: [mg9359] Integrate[ ] returns If[ ] function; how to say it's True?
- From: seanross at worldnet.att.net
- Date: Sun, 2 Nov 1997 01:02:26 -0500
- Sender: owner-wri-mathgroup at wolfram.com
AES wrote: > > Doing an Integrate[ ] returns an If[condition,a,b] result, with > complicated expressions for condition, a, and b. > > I want to get B as input for the next cell (automatically, not by just > copying it by hand). > > How can I get at the "parts" of the If[ ] statement, or use it in a > subsequent Input[ ] cell with condition set equal to True? Two Ways: One, you can use the new Assumptions option in Integrate to specify that a certain variable is Real(Assumptions->Im[x]==0), positive (Assumptions->x>0) or both(Assumptions->{Im[x]==0,x>0}. Two, you can specifically set the inequality equal to True or False as appropriate. For Example: Integrate[Exp[-t^2/T^2],{t,-Infinity,Infinity}] returns If[Re[T^2>0,Sqrt[Pi] Sqrt[T^2],Integrate[Exp[-t^2/T^2],{t,-Infinity,Infinity}]]. But, Unprotect[Greater]; Re[T^2]>0=True; Protect[Greater]; PowerExpand[Integrate[Exp[-t^2/T^2],{t,-Infinity,Infinity}]] Returns Sqrt[Pi]T.