[Maxima] integral of cos(1/x) with range doesn't work.

Stavros Macrakis macrakis at alum.mit.edu
Tue Apr 8 13:45:40 CDT 2008


On Tue, Apr 8, 2008 at 10:47 AM, J.C. Pizarro <jcpiza at gmail.com> wrote:
>  (%i1) integrate(cos(1/x), x);
>  Why? Where is the failure of that it doesn't compute?

Maxima's specialty is symbolic computation. By default, most
mathematical operations in Maxima are exact symbolic calculations.  If
Maxima cannot express a result in an exact form, it leaves it as is.
For example, it knows that sin(%pi) is 0, and sin(%pi/3) is sqrt(3)/2,
but it cannot express sin(2) or sin(%pi/17) in an exact form, so it
leaves them as is.

Similarly, it does not know an exact expression for
integrate(cos(1/x),x,0,2/%pi). It does however have functions for
numeric calculation of integrals.  Try ?? quad_q to get more
information on them.  For example,

        quad_qag(cos(1/x),x,0,2/%pi,6,1.0e-5,10000)

yields

        [- 0.2, 2.000158E-6, 854061, 0]

which makes it look like the answer is exactly -1/5 -- but is that
true?  It doesn't seem likely, but I don't know.

            -s


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