Partial integration with maxima
- Subject: Partial integration with maxima
- From: Michel Gosse
- Date: Wed, 14 Sep 2005 21:21:06 +0200
What do you think of :
(C1) intpart(u,v,a,b):=subst(x=b,integrate(u,x))*subst(x=b,v)-
subst(x=a,integrate(u,x))*subst(x=a,v)-integrate(integrate(u,x)*diff(v,x),x,a,b);
(D1) intpart(u,v,a,b):=SUBSTITUTE(x=b,INTEGRATE(u,x)) SUBSTITUTE(x=b,v) -
SUBSTITUTE(x=a,INTEGRATE(u,x)) SUBSTITUTE(x=a,v) - INTEGRATE(INTEGRATE(u,x)
DIFF(v,x),x,a,b)
Examples :
(C2) 'integrate(x*log(x),x,1,%e)=intpart(x,log(x),1,%e);
(C4) 'integrate(x*exp(2*x),x,0,1)=intpart(x,exp(2*x),0,1);
(D5) 'integrate(x^n*sin(x),x,0,%pi/2)=intpart(x^n,sin(x),0,%pi/2);
Maxima will not do the job alone...
Le mercredi 14 Septembre 2005 13:32, Marc Hodapp a écrit :
> Hi everybody,
>
> how can I perform an integration by parts like
>
> b b
> / b /
>
> | u'*v dx = [u*v] - | u*v' dx
>
> / a /
> a a
>
> with maxima? u and v are functions of x by the way.
>
> Many thanks in advance.
>
> Marc Hodapp
>
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