On Friday 25 April 2003 23:28, Raymond Toy wrote:
> Felix> 2. Maxima returns a non continuous indefinite integral:
> Felix> (C214) ratsimp(integrate(integrand,x));
> Felix> (D214) 2*ATAN((SQRT(2)*SIN(x)+COS(x)+1)/(COS(x)+1))
>
> In these kinds of integrals, don't you always have to be careful about
> what branch of atan should be used?
>
> This is probably why ldefint returns 0 since d214 is %pi/2 for both x
> = 0 and x = 2*%pi.
As far as I can see the result d214 is mathematically incorrect because:
d214 is non contiguos at (2*n-1)*%pi.
=> d214 is underivable at (2*n-1)*%pi
=> d214 is not the antiderivative of integrand (or only the antiderivative
on a limited range for x).
A correct result would be something like
(if (remainder(u-%pi,2*%pi) = 0) then 0 else d214)
+ 2*%pi*entier((u-%pi) / (2*%pi))
Felix