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Re: definite integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg49361] Re: definite integral
*From*: "Curt Fischer" <crf3 at po.cwru.edu>
*Date*: Fri, 16 Jul 2004 06:06:41 -0400 (EDT)
*References*: <cd5ooi$b37$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Josh:
You need to use Evaluate[] inside your NIntegrate command. For an trivial
example (which has the advantage of being able to be checked symbolically)
see below:
In[1]:=
sol=NDSolve[{y[0]==1,v[0]==0,y'[t]==v[t],v'[t]==-1},{y[t],v[t]},{t,0,1}]
Out[1]=
{{y[t]\[Rule]
InterpolatingFunction[{{0.,1.}},<>][t],v[t]\[Rule]InterpolatingFunction[\
{{0.,1.}},<>][t]}}
In[2]:=
Plot[Evaluate[y[t]/.sol],{t,0,1}]
Out[2]=
?Graphics?
In[3]:=
NIntegrate[Evaluate[y[t]/.sol],{t,0,1}]
Out[3]=
{0.833333}
Here's how you can check that this answer is correct (at least in this
simple case):
In[4]:=
check=DSolve[{y[0]==1,v[0]==0,y'[t]==v[t],v'[t]==-1},{y[t],v[t]},t][[1]]
Out[4]=
\!\({y[t] \[Rule] 1\/2\ \((2 - t\^2)\), v[t] \[Rule] \(-t\)}\)
In[5]:=
Integrate[y[t]/.check,{t,0,1}]
Out[5]=
\!\(5\/6\)
Josh wrote:
> from the solution of a system of 2 differential equations
>
> sol=NDSolve[{v'[t]==10^3*i[t],
> y'[t]== etc...
>
> I get the solution y[t] for t \in [0,1], and I can plot it with the
> command:
>
> Plot[Evaluate[y[t]/.sol],{t,0,0.5}, PlotRange->{-2,2}]
>
> but I have also to compute the definite integral of y[t], between 0
> and
> 0.1, how can I do?
>
> Thanks, Josh.
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