When I enter:
assume(1-x^2>0)
and then:
integrate( integrate(x^2+y^2, y, -sqrt(1-x^2), sqrt(1-x^2)), x,-1,1)
I still get the error:
..... <lots of stuff>.....
TypeError: Error executing code in Maxima
CODE:
sage191 : integrate(sage188,sage11,sage189,sage190)$
Maxima ERROR:
Defint: Lower limit of integration must be real.
I know I can do the integral much more easily with a change of
variables, but I want to do it this way.
When I try to convince it that 1-x^2 really is nonnegative, with:
integrate( integrate(x^2+y^2, y, -sqrt(abs(1-x^2)), sqrt(abs(1-x^2))),
x,-1,1)
I get the answer 0. Just to convince myself that I'm not crazy, I
did:
Integrate[Integrate[x^2+y^2, {y, -Sqrt[Abs[1-x^2]], Sqrt[Abs[1-x^2]]}],
{x,-1,1}]
in Mathematica, and it gives the correct answer of pi/2.
Is there some way in which I can tell Maxima that 1-x^2 really is
nonnegative, and is there a reason why it's giving an answer of 0?
I entered all these commands through the notebook of sage 3.4.2
running on Ubuntu 9.04.
-Alden
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