#11164: Integral of sin(x)/x gives false result.
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Reporter: benreynwar | Owner: burcin
Type: defect | Status:
Priority: major | needs_info
Component: calculus | Milestone:
Keywords: | Resolution:
Authors: | Merged in:
Report Upstream: Fixed upstream, in a later | Reviewers:
stable release. | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> {{{
> > eq = sin(x)/x
> > integrate(eq, x, -1e-6, 1e6)
> -3.14159065359
> }}}
> I expected an answer of about 2e-6.
New description:
{{{
> eq = sin(x)/x
> integrate(eq, x, -1e-6, 1e-6)
-3.14159065359
}}}
I expected an answer of about 2e-6.
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Comment (by tscrim):
In 6.3.beta4 (so with #13973), I get:
{{{
sage: eq = sin(x) / x
sage: integrate(eq, x, -1e-6, 1e-6)
-I*Ei(1/1000000*I) + I*Ei(-1/1000000*I)
sage: _.n()
3.14159465358979
sage: integrate(eq, x, -1e-12, 1e-12)
-I*Ei(1/1000000000000*I) + I*Ei(-1/1000000000000*I)
sage: _.n()
3.14159265359179
}}}
Something bad happens with the integration computation when crossing over
0 as we have:
{{{
sage: integrate(eq, x, 1e-12, 1e-6)
-1/2*I*Ei(1/1000000*I) + 1/2*I*Ei(1/1000000000000*I) -
1/2*I*Ei(-1/1000000000000*I) + 1/2*I*Ei(-1/1000000*I)
sage: _.n()
9.99999000050877e-7
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/11164#comment:10>
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