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Topic: hard integral
Replies: 8   Last Post: Feb 23, 2014 2:18 PM

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G. A. Edgar

Posts: 2,497
Registered: 12/8/04
Re: hard integral
Posted: Feb 21, 2014 8:53 AM
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In article <210220140621150813%edgar@math.ohio-state.edu.invalid>, G.
A. Edgar <edgar@math.ohio-state.edu.invalid> wrote:

> In article <le77hs$7ep$1@speranza.aioe.org>, Nasser M. Abbasi
> <nma@12000.org> wrote:
>

> > Maple 17
> > ----------
> >
> > (*can do direct definite integration but gives wrong answer?*)
> > z:=arcsin(sqrt(x))/(x^4-2*x^3+2*x^2-x+1);
> > r:=int(z,x=0..1):
> > evalf(r);
> > -.894336814301231-.670856586950946*I

>
> If you do A := int(z,x): plot(Re(A),x=0..1);
>
> you will see why Maple gets the wrong answer for this. It has
> discontinuities in its antiderivative.


We can do it in Maple with more work ...
one discontinuity is between 0.22487 and 0.22488, the other is
between 0.77512 and 0.77513 ... so

B:=int(z,x): b:=unapply(B,x):
b(1.0)-b(0.77513)+b(0.77512)-b(0.22488)+b(0.22487)-b(0.0);
0.9095024586-0.10e-8*I

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/



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