On Tuesday, July 22, 2014 2:04:01 AM UTC-7, Craig E Larson wrote:
>
> I am getting an error that I don't understand for the following definite 
> integral.
>
> sage: integral(sqrt(1+(9*cos(3*x)^2)),0,pi/2)
>
> This is definitely real on its domain and under the square-root is always 
> positive. Nevertheless, I get the error:
>
Maxima proper doesn't produce an error but doesn't do anything useful with 
the integral:

 (%i1) display2d: false;
(%o1) false
(%i2) integrate(sqrt(1+cos(x)^2),x,0,%pi);
(%o2) 'integrate(sqrt(cos(x)^2+1),x,0,%pi)

but when we load abs_integrate (which sage does) the error occurs:

(%i3) load(abs_integrate);
(%o3) 
"/usr/local/sage/sage-6.0/local/share/maxima/5.29.1/share/contrib/integration/abs_integrate.mac"
(%i4) integrate(sqrt(1+cos(x)^2),x,0,%pi);

sign: argument cannot be imaginary; found %i

One could consider reporting this upstream.

On the plus side: it's not caused by `domain: complex` this time.

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