Multiple Integration Issues
John Travis
Mississippi College
Compute:
$ \int_{0}^{2}\int_{y^2}^{4}f(x,y)dx dy $
or
$ \int_{0}^{4}\int_{0}^{\sqrt{x}}f(x,y)dy dx $
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Traceback (click to the left of this block for traceback) ... Is (y-2)*(y+2) positive, negative or zero? Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_28.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("IyAgV2UgZmlyc3QgdHJ5IHRvIGludGVncmF0ZSBkaXJlY3RseSB1c2luZyB0aGUgc2FnZSBjb21tYW5kCgpnID0gaW50ZWdyYXRlKGYseCx5XjIsNCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpJiQI9y/___code___.py", line 4, in <module> exec compile(u'g = integrate(f,x,y**_sage_const_2 ,_sage_const_4 ) File "", line 1, in <module> File "/home/sageserver/sage-8.7/local/lib/python2.7/site-packages/sage/misc/functional.py", line 753, in integral return x.integral(*args, **kwds) File "sage/symbolic/expression.pyx", line 12361, in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:63599) File "/home/sageserver/sage-8.7/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 817, in integrate return definite_integral(expression, v, a, b, hold=hold) File "sage/symbolic/function.pyx", line 998, in sage.symbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.cpp:11841) File "sage/symbolic/function.pyx", line 487, in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6820) File "sage/symbolic/function.pyx", line 1086, in sage.symbolic.function.BuiltinFunction._evalf_or_eval_ (build/cythonized/sage/symbolic/function.cpp:12980) File "/home/sageserver/sage-8.7/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 183, in _eval_ return integrator(*args) File "/home/sageserver/sage-8.7/local/lib/python2.7/site-packages/sage/symbolic/integration/external.py", line 34, in maxima_integrator result = maxima.sr_integral(expression, v, a, b) File "/home/sageserver/sage-8.7/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py", line 817, in sr_integral self._missing_assumption(s) File "/home/sageserver/sage-8.7/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py", line 1053, in _missing_assumption raise ValueError(outstr) ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((y-2)*(y+2)>0)', see `assume?` for more details) Is (y-2)*(y+2) positive, negative or zero? |
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Traceback (click to the left of this block for traceback) ... ValueError: Integral is divergent. Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_27.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("STMgPSBpbnRlZ3JhdGUocipoLHIsMCxjb3ModCkvc2luKHQpXjIpCnNob3coSTMpCkk0ID0gaW50ZWdyYXRlKEkxLHQsYyxwaS8yKQpzaG93KEk0KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpkplZff/___code___.py", line 5, in <module> I4 = integrate(I1,t,c,pi/_sage_const_2 ) File "/home/sageserver/sage-6.7/local/lib/python2.7/site-packages/sage/misc/functional.py", line 663, in integral return x.integral(*args, **kwds) File "sage/symbolic/expression.pyx", line 10712, in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:52942) File "/home/sageserver/sage-6.7/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 761, in integrate return definite_integral(expression, v, a, b, hold=hold) File "sage/symbolic/function.pyx", line 994, in sage.symbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.cpp:10866) File "sage/symbolic/function.pyx", line 502, in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6802) File "sage/symbolic/function.pyx", line 1065, in sage.symbolic.function.BuiltinFunction._evalf_or_eval_ (build/cythonized/sage/symbolic/function.cpp:11523) File "/home/sageserver/sage-6.7/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 176, in _eval_ return integrator(*args) File "/home/sageserver/sage-6.7/local/lib/python2.7/site-packages/sage/symbolic/integration/external.py", line 23, in maxima_integrator result = maxima.sr_integral(expression, v, a, b) File "/home/sageserver/sage-6.7/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py", line 782, in sr_integral raise ValueError("Integral is divergent.") ValueError: Integral is divergent. |
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