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integral should not be zero

asked 2014-10-19 17:44:26 -0500

jllb gravatar image

updated 2014-10-20 12:23:41 -0500

tmonteil gravatar image
F = sqrt((cos(x) - 1)^2 + sin(x)^2)
F.integrate(x, 0, 2*pi)

yields 0, the expected answer is 8.

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answered 2014-10-20 08:20:26 -0500

kcrisman gravatar image

Indeed.

sage: F.nintegrate(x,0,2*pi)
(8.0, 8.881784197001255e-14, 21, 0)

Maxima does this correctly internally.

(%i2) integrate( sqrt((cos(x) - 1)^2 + sin(x)^2), x, 0, 2*%pi);
(%o2)                                  8

But

(%i5) load(abs_integrate);
(%o5) /Users/.../sage/local/share/maxima/5.34.1/share/contr\
ib/integration/abs_integrate.mac
(%i6) integrate( sqrt((cos(x) - 1)^2 + sin(x)^2), x, 0, 2*%pi);
(%o6)                                  0

So this seems to be a bug in that package.

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kcrisman gravatar imagekcrisman ( 2014-10-20 08:36:13 -0500 )edit

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Asked: 2014-10-19 17:44:26 -0500

Seen: 132 times

Last updated: Oct 20 '14