# [Maxima] Integration question (definite integral)

Raymond Toy toy.raymond at gmail.com
Tue Aug 21 18:40:25 CDT 2007

```max.e.brown at gmail.com wrote:
> Rupert Swarbrick <rupert.swarbrick at lineone.net> writes:
>
>
>> Well, log(sin(0)) = log(0) = -infinity, so maybe Maxima's right?
>>
>
> Maybe I should clarify. What puzzles me is why Maxima wants to know
> whether sin(x) is positive, negative or zero, in order to determine
> that the integral is divergent.
>
> As you say, I would expect
> log(sin(%pi/2)) - log(sin(0)) = log(1) - log(0) = 0 - (-inf) = inf
> or something to that effect. To me it seems that it is not necessary
> to state that `sin(x) > 0' (which isn't really all that correct) to
> deduce that.
>
>
You assume that maxima is computing the antiderivative and substituting
the limits.  While maxima can do that, other methods are normally tried
first.  These methods usually involve transforming the integral to
another form and performing contour integration and using residue theory
to compute it.

I'd have to look more closely to find out what method is being tried.

But it is a shortcoming of maxima that it sometimes asks questions that
are irrelevant.

If you like, you can file a bug report saying that maxima asks
irrelevant questions.

Ray
```