# [Maxima] An integration bug

Milan Lukic milan at eskimo.com
Tue Nov 20 07:10:40 CST 2007

```Robert,
Thank you for the explanation. I did not know that nouns would turn
trig and hyperbolic function values into floats. Also
'integrate(...),integrate; is a new idea to me.
Milan

* Robert Dodier &lt;robert.dodier at gmail.com&gt; [2007-11-19 22:14:44 -0700]:

> On 11/19/07, Milan Lukic <milan at eskimo.com> wrote:
>
> > I am calculating the arc length of a piece of parabola. Here is the
> > integral,
> >
> > 'integrate(sqrt(9*x^2+37),x,0,2);
> >
> > I would like Maxima to do the problem using the following
> > substitution:
> >
> > changevar(%,3*x=sqrt(37)*sinh(t),t,x);
> >
> > Maxima returns,
> >
> > 37*('integrate(cosh(t)*sqrt(sinh(t)^2+1),t,0,asinh(6/sqrt(37))))/3
> > %,nouns;
>
> Milan, it looks like Maxima is behaving as intended here.
> asinh(6/sqrt(37)), nouns; => floating point number
> which then causes integrate to forget about trying to use
> exact constants. All trigonometric and hyperbolic functions have
> that behavior, that foo(x), nouns; => float when x is a number.
>
> To tell Maxima to verbify only integrate,
> 37*('integrate(cosh(t)*sqrt(sinh(t)^2+1),t,0,asinh(6/sqrt(37))))/3, integrate;
>   => 37*%e^-(2*asinh(6/sqrt(37)))
>   *(%e^(4*asinh(6/sqrt(37)))+4*asinh(6/sqrt(37))
>                               *%e^(2*asinh(6/sqrt(37)))-1) /24
> %, numer;
>  => 13.91960941686494
>
> I think that verbify => numerical evaluation has come up before.
> It certainly is subtle. But we haven't changed anything about it;
> maybe it is time to revisit that topic.
>
> Robert Dodier
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--
```

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