Status: Valid
Owner: ----
Labels: Type-Defect Priority-High WrongResult Integration
New issue 4031 by [email protected]: Definite integral returns an answer
with indefinite integrals
http://code.google.com/p/sympy/issues/detail?id=4031
In [1]: var("i L a b")
Out[1]: (i, L, a, b)
In [2]: integrand = cos(pi*i*x/L)**2/(a + b*x)
In [3]: integrand = integrand.rewrite(exp)
In [4]: integrate(integrand, (x, 0, L))
Out[4]:
⌠
⌠ ⎮ 4⋅ⅈ⋅π⋅i 2⋅ⅈ⋅π⋅i
⎮ 1 ⎮ ℯ + 2⋅ℯ + 1
- ⎮ ─ dx + ⎮ ───────────────────────────── dx
⎮ a ⎮ 2⋅ⅈ⋅π⋅i 2⋅ⅈ⋅π⋅i
⌡ ⎮ 4⋅L⋅b⋅ℯ + 4⋅a⋅ℯ
⌡
The answer is obviously wrong (it should not depend on x).
Also, I don't know if this is related, but integrate seems to be quite
inefficient. I put a print statement at the top of integrate() to print the
args, and I got
In [4]: integrate(integrand, (x, 0, L))
((exp(I*pi*i*x/L)/2 + exp(-I*pi*i*x/L)/2)**2/(a + b*x), (x, 0, L))
(4/(4*a + 4*b*x) - 1/(2*a + 2*b*x), x)
(1/(2*a + 2*b*x), x)
(1/(4*a + 4*b*x), x)
(1/(4*a + 4*b*x), x)
(0, x)
(1/(4*a + 4*b*x), x)
(1/(4*a + 4*b*x), x)
(1/(4*a + 4*b*x), x)
Out[4]:
⌠
⌠ ⎮ 4⋅ⅈ⋅π⋅i 2⋅ⅈ⋅π⋅i
⎮ 1 ⎮ ℯ + 2⋅ℯ + 1
- ⎮ ─ dx + ⎮ ───────────────────────────── dx
⎮ a ⎮ 2⋅ⅈ⋅π⋅i 2⋅ⅈ⋅π⋅i
⌡ ⎮ 4⋅L⋅b⋅ℯ + 4⋅a⋅ℯ
⌡
In other words, it is computing that same integral (1/(4*a + 4*b*x)) six
times.
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