Dear Ray,
thanks for reply.
Raymond Toy wrote:
> >>>>> "Valery" == Valery Pipin <pip at iszf.irk.ru> writes:
>
> Valery> This bug is marked as solved
>
> >> * 1044318: defint(1/(sin(x)^2+1),x,0,3*%pi) wrong
>
> Valery> Indeed defint(1/(sin(x)^2+1),x,0,3*%pi) give the right answer
> -> 3 sqrt(2) Valery> pi/2.
>
> Valery> however
> Valery> defint(1/(a^2*sin(x)^2+1),x,0,3*%pi) still gives 0
>
> Does it? Here's what I get:
>
> (%i9) integrate(1/(1+a^2*sin(x)^2),x,0,3*%pi);
> 2 2
> Is a (a sqrt(a + 1) + sqrt(a )) positive, negative, or zero?
>
> pos;
> 2 2
> Is 2 sqrt(a + 1) - a - 2 positive, negative, or zero?
>
> neg;
> 2 2
> Is abs(a) - sqrt(2 sqrt(a + 1) + a + 2) positive, negative, or zero?
>
> neg;
> 2 2
> Is abs(a) - sqrt(- 2 sqrt(a + 1) + a + 2) positive, negative, or zero?
>
> pos;
> 3 %pi
> (%o9) ------------
> 2
> sqrt(a + 1)
>
> (I answered the questions assuming a = 1).
> And for a = 1, we get right answer.
the problem is how to make maxima to evaluate automaticaly.
after declaration
(declare(a,real), assume(a>0, sqrt(2*sqrt(a^2+1)+a^2+2)-a > 0,
2*sqrt(a^2+1)-a^2-2 < 0, sqrt(-2*sqrt(a^2+1)+a^2+2)-a < 0);
maxima still ask about sign of
sqrt(-2*sqrt(a^2+1)+a^2+2)-a