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Re: wrong solution for double integral of piecewise function?

• To: mathgroup at smc.vnet.net
• Subject: [mg96987] Re: wrong solution for double integral of piecewise function?
• From: Tom Roche <tlroche at gmail.com>
• Date: Sun, 1 Mar 2009 04:55:37 -0500 (EST)
• References: <gob80u$g9q$1@smc.vnet.net>

Tom Roche Feb 28, 6:43 am
>> Solve[
>>   First[
>>     Integrate[
>>       Integrate[
>>         f[\[Chi], \[Psi]], {\[Psi], -\[Infinity], \[Infinity]}
>>       ],
>>         {\[Chi], -\[Infinity], \[Infinity]}
>>     ]
>>   ] == 1, k
>> ]

>> [gets]

>> (2) {{k -> -(1/((a - b)^2 (-1 + UnitStep[a - b])))}}

Bob Hanlon
> When you integrated by hand you assumed that b > a, Mathematica
> gives a more complicated result since it does not make that
> assumption unless you tell it to do so.

and he points out that the proper way to do this is by wrapping an
Assuming around the procedure above:

Assuming[{b > a},
  Solve[
    First[
      Integrate[
        Integrate[
          f[\[Chi], \[Psi]], {\[Psi], -\[Infinity], \[Infinity]}
        ],
          {\[Chi], -\[Infinity], \[Infinity]}
      ]
    ] == 1, k
  ]
]

produces

{{k -> 1/(a - b)^2}}

Thanks!