Attached is the 'edit' view of my worksheet. When I changed the lower
bound of the definite integral from 0.0001415 to 0.0001414, we got
into trouble.
Elizabeth
------------------------------------------------------------------------------------------------------------
integration_exercise
system:sage
{{{id=0|
x,y=var('x,y')
f=log(x^2+y^2)
integrate(f,x)
///
x*log(y^2 + x^2) - 2*(x - atan(x/y)*y)
}}}
{{{id=11|
assume(y^2>1)
integrate(f,x,0.0001415,1.)
///
1.00000000000000*log(1.00000000000000*y^2 + 1.00000000000000) -
0.0001415000000000000000*log(1.00000000000000*y^2 +
0.000000020022250000000000000000) +
2.00000000000000*atan(1.00000000000000/y)*y -
2.00000000000000*atan(0.0001415000000000000000/y)*y - 1.99971700000000
}}}
{{{id=16|
assume(y^2<1)
integrate(f,x,0.0001415,1.)
///
1.00000000000000*log(1.00000000000000*y^2 + 1.00000000000000) -
0.0001415000000000000000*log(1.00000000000000*y^2 +
0.000000020022250000000000000000) +
2.00000000000000*atan(1.00000000000000/y)*y -
2.00000000000000*atan(0.0001415000000000000000/y)*y - 1.99971700000000
}}}
{{{id=17|
assume(y^2==1)
integrate(f,x,0.0001415,1.)
///
1.00000000000000*log(1.00000000000000*y^2 + 1.00000000000000) -
0.0001415000000000000000*log(1.00000000000000*y^2 +
0.000000020022250000000000000000) +
2.00000000000000*atan(1.00000000000000/y)*y -
2.00000000000000*atan(0.0001415000000000000000/y)*y - 1.99971700000000
}}}
{{{id=19|
assume(y^2>1)
integrate(f,x,0.0001414,1.)
///
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/yip/sage_notebook/worksheets/admin/10/code/47.py", line
5, in <module>
exec
compile(ur'integrate(f,x,RealNumber(\u00270.0001414\u0027),RealNumber(\u00271.\u0027))'
+ '\n', '', 'single')
File "/local/sage-2.8.5.1/data/extcode/sage/", line 1, in <module>
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
calculus/functional.py", line 175, in integral
return f.integral(*args, **kwds)
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
calculus/calculus.py", line 1652, in integral
return self.parent()(self._maxima_().integrate(v, a, b))
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/maxima.py", line 1391, in integral
return I(var, min, max)
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/expect.py", line 884, in __call__
return self._obj.parent().function_call(self._name, [self._obj] +
list(args))
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/expect.py", line 831, in function_call
return self.new("%s(%s)"%(function, ",".join([s.name() for s in
args])))
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/expect.py", line 733, in new
return self(code)
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/maxima.py", line 376, in __call__
return Expect.__call__(self, x)
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/expect.py", line 678, in __call__
return cls(self, x)
File "/local/sage-2.8.5.1/local/lib/python2.5/site-packages/sage/
interfaces/expect.py", line 919, in __init__
raise TypeError, x
TypeError: Computation failed since Maxima requested additional
constraints (use assume):
Is (y-1)*(y+1) positive, negative, or zero?
}}}
{{{id=20|
}}}
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