       Re: use of SetDelayed functions in Plot and Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg44601] Re: [mg44585] use of SetDelayed functions in Plot and Solve
• From: Anton Antonov <antonov at wolfram.com>
• Date: Mon, 17 Nov 2003 03:38:36 -0500 (EST)
• References: <200311150705.CAA11421@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

(1)
In the first, SetDelayed input you use NIntegrate, in the second, Set
input you use Integrate. If you use Integrate in the SetDelayed input
you will get the plot.

NIntegrate is a numerical function, so at the time it is invoked all of
its arguments should be numbers or evaluate to numbers. When you use the
definitions

Clear[s, i, k];
s[t_] := NIntegrate[t^2 - z*Log[t], {z, 0, k[t]}];
i[t_] := D[s[t], t] /. {k[t] -> 2t, k'[t] -> Sin[t]};

the command D[s[t],t] in i[t_] trys to evaluate NIntegrate with a
symbolic variable range. With Integrate, of course, symbolic ranges are
fine.

(2)
As for the Solve part, you can try FindRoot, instead of Solve.

In:=
Clear[s, i];
s[t_] := Integrate[t^2 - z*Log[t], {z, 0, k[t]}];
i[t_] := D[s[t], t] /. {k[t] -> 2t, k'[t] -> Sin[t]};

In:=FindRoot[i[t]==300,{t,1}]
Out={t->8.48795}

Anton Antonov
Wolfram Research, Inc.

Mukhtar Bekkali wrote:

>Why can't I plot the function and find the solution to the equation below
>using SetDelayed functions?  Below is just an example, the real functions
>are symbolically non-integrable.
>
>s[t_] :=NIntegrate[t^2 - z*Log[t] , {z, 0, k[t]}]
>i[t_] := D[s[t],t] /. {k[t] ->2t,k'[t]->Sin[t]}
>Plot[i[t], {t, 1, 10}]
>Solve[i[t]==300, t]]
>
>
>All I get is an empty graph because I have "not machine real size numbers"
>and my equation "appears to be solved essentially in non-algebraic way".
>If I rewrite the code using simple Set I get my graph and solutions.
>
>s=Integrate[t^2 - z*Log[t] , {z, 0, k[t]}]
>i=D[s,t] /. {k[t]->2t,k'[t]->Sin[t]}
>Plot[i, {t, 1, 10}]
>Solve[i==300, t]]
>
>Very confused. Thanks, Mukhtar Bekkali
>
>
>
>

```

• Prev by Date: Re: Automatic comment coloring
• Next by Date: Re: Readability confuses mathematica?
• Previous by thread: use of SetDelayed functions in Plot and Solve
• Next by thread: Re: use of SetDelayed functions in Plot and Solve