On Dec 4, 2008, at 3:57 PM, Vijay wrote:
Hi: I am trying to evaluate a double integral (since I cannot put
LaTeX, the 'S' below
stands for the integral sign:)
1 sqrt(x)
S S 4xy - y^3 dy dx
0 x^3
This is what I put into sage:
sage: var('x,y')
(x, y)
sage: f=4*x*y-y^3
sage: print f
3
4 x y - y
sage: print integrate(integrate(f,y,x^3,x^0.5),y,0,1)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/vkg/sage-3.1.1/<ipython console> in <module>()
/home/vkg/sage-3.1.1/local/lib/python2.5/site-packages/sage/calculus/
functional.
py in integral(f, *args, **kwds)
252 """
253 try:
--> 254 return f.integral(*args, **kwds)
255 except ValueError, err:
256 raise err
/home/vkg/sage-3.1.1/local/lib/python2.5/site-packages/sage/calculus/
calculus.py
in integral(self, v, a, b)
2523 raise ValueError, "Integral is divergent."
2524 else:
-> 2525 raise TypeError, error
2526
2527
TypeError: Computation failed since Maxima requested additional
constraints (use
assume):
Is x positive or negative?
Am I doing something wrong here?
This may be a bug in Maxima, because it looks like it can do the indefinite integral. However, any integral that requires feedback from the user during the integration, won't work from Sage. This has caused me problems with my integral test suite.
Also, in integrate(integrate(f,y,x^3,x^0.5),y,0,1)you're integrating with respect to y twice. You can always try to carry out the indefinite integral and then evaluate at the end points. That appears to
work so I find it interesting that Maxima can't integrate the definite integral. Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo http://www.linkedin.com/in/timlahey
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