Status: Accepted
Owner: jochen.voss
Labels: Type-Defect Priority-Medium WrongResult Integration

New issue 1428 by jochen.voss: wrong result for integral of  
sin(k*x)*sin(m*x) over [0,pi]
http://code.google.com/p/sympy/issues/detail?id=1428

Hi,

current sympy (from git) returns a wrong result for me when I integrate
then function sin(k*x)*sin(m*x) over the interval [0,pi]:

--------------------------------------------------
v...@automatix [~/sympy] bin/isympy
Python 2.6.2 console for SymPy 0.6.5-git

These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z = symbols('xyz')
>>> k, m, n = symbols('kmn', integer=True)
>>> f, g, h = map(Function, 'fgh')

Documentation can be found at http://sympy.org/

In [1]: integrate(sin(k*x)*sin(m*x),(x,0,pi))
Out[1]: 0

In [2]: integrate(sin(k*x)*sin(k*x),(x,0,pi))
Out[2]:
π
─
2

In [3]: m-k
Out[3]: m - k

The result Out[1] should only be 0 if m != k.  For m == k we should get
pi/2 as in Out[2].  The third expression shows that sympy does not
generically assume m == k, since m-k is not simplified to 0.

I hope this helps,
Jochen

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