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Re: Differentiating with respect to an expression

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rouben@shadow.(none) (Rouben Rostamian) writes:

> In article <m3uatb$st7$1@speranza.aioe.org>,
> Nasser M. Abbasi <nma@12000.org> wrote:
>>On 11/11/2014 5:39 PM, none Rouben Rostamian wrote:
>>
>>> Thanks much, Joe, this is exactly what I was hoping for.
>>> I had no idea about frontend() or the Physics package.
>>>
>>> This brings up a somewhat related question.  Doing
>>>     frontend(int, [x(t)^2, x(t)]);
>>> we get x(t)^3/3, which is fine.  The following, however,
>>> issues an Error message:
>>>      frontend(int, [x(t)^2, x(t)=a..b]);
>>>
>>> Is there a way to get that to work too?
>>>
>>> Rouben
>>>
>>
>>I do not use frontend() either. But if all else fails, you
>>can simply use calculus
>>
>>------------------------------
>>restart;
>>f := frontend(int,[x(t)^2, x(t)]);
>>f := unapply(f,t);
>>limit(f(t),t=b)-limit(f(t),t=a);
>>-------------------------
>>
>>     (1/3)*x(b)^3-(1/3)*x(a)^3
>
> Hi Nasser, that's good but it's not exactly what
> I had asked.  Your result integrates over t=a..b.
> I wanted x(t)=a..b, but that's easy to fix:
> f := frontend(int,[x(t)^2, x(t)]);
> eval(f, x(t)=b) - eval(f, x(t)=a);
>
> This technique, however, does not work in a more complex case.
> For instance, let's write x' and x'' for the first and second
> derivatives of x.  We want to integrate x'' * x' * x^2 with
> respect to x.  So we do:
>
>     frontend(int, [diff(x(t),t,t)*diff(x(t),t)*x(t)^2, x(t)]);
>
> and we get the expected 1/3 * x'' * x' * x^3.
>
> Now, how do we do the corresponding definite integral
> where x(t)=a..b ?  The expected answer is
> 1/3 * x''(t) * x'(t) * (b^3 - a^3).

frontend(int, [diff(x(t),t,t)*diff(x(t),t)*x(t)^2, x(t)=a..b], [{`+`,`*`,`^`,`=`,`..`},{}]);  
   1/3*diff(x(t),`$`(t,2))*diff(x(t),t)*(-a^3+b^3)

-- 
Joe Riel

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Thread

Differentiating with respect to an expression rouben@shadow.(none) (Rouben Rostamian) - 2014-11-11 22:10 +0000
  Re: Differentiating with respect to an expression Joe Riel <joer@san.rr.com> - 2014-11-11 14:35 -0800
    Re: Differentiating with respect to an expression rouben@shadow.(none) (Rouben Rostamian) - 2014-11-11 23:39 +0000
      Re: Differentiating with respect to an expression "Nasser M. Abbasi" <nma@12000.org> - 2014-11-11 18:50 -0600
        Re: Differentiating with respect to an expression "Nasser M. Abbasi" <nma@12000.org> - 2014-11-11 19:44 -0600
        Re: Differentiating with respect to an expression rouben@shadow.(none) (Rouben Rostamian) - 2014-11-12 01:55 +0000
          Re: Differentiating with respect to an expression Joe Riel <joer@san.rr.com> - 2014-11-11 18:00 -0800
            Re: Differentiating with respect to an expression Joe Riel <joer@san.rr.com> - 2014-11-11 18:03 -0800
              Re: Differentiating with respect to an expression rouben@shadow.(none) (Rouben Rostamian) - 2014-11-12 02:44 +0000
                Re: Differentiating with respect to an expression Joe Riel <joer@san.rr.com> - 2014-11-11 19:16 -0800
                Re: Differentiating with respect to an expression rouben@shadow.(none) (Rouben Rostamian) - 2014-11-12 04:53 +0000
      Re: Differentiating with respect to an expression Joe Riel <joer@san.rr.com> - 2014-11-11 17:45 -0800
        Re: Differentiating with respect to an expression Joe Riel <joer@san.rr.com> - 2014-11-11 17:52 -0800
        Re: Differentiating with respect to an expression rouben@shadow.(none) (Rouben Rostamian) - 2014-11-12 02:03 +0000

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