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Integrate question
10-19-2017, 05:03 PM (This post was last modified: 10-19-2017 05:22 PM by toshk.)
Post: #15
RE: Integrate question
(10-19-2017 03:08 PM)DrD Wrote:  I like your analysis!

However, (and this part is the same as my last post):
[CAS]
a:=int(cos(2*x)^3*sin(2*x)^5,x); // From the original example, [CAS] var a becomes: -3*cos(2*x)^8+8*cos(2*x)^6-6*cos(2*x)^4)/48
b:=-(3*sin(2*x)^8-4*sin(2*x)^6)/48; // result obtained by hand, (and wxMaxima)

Now try this:
subst(a,x = 0.58)-subst(b,x = 0.58); // difference =āˆ’2.08333333333eāˆ’2

This demonstrates that they do not produce the same result, regardless of the difference being a constant, (OR any constant being valid for an indefinite integral).

Also, by hand, or the wxMaxima result is better than the CAS/xcas result, in that it recognizes that you can use ANY constant, not just one particular constant offered up by CAS, (-1/48, in this case).

Notice, these are simply 'as entered' examples, (no massaging attempts to format the results, this time). There is a constant bias on the [CAS] side, which needs to be modeled, if simulating a PLC, for example. The constants accumulate with multi-processing, so the output routine must chase the resulting error term.

-Dale-
it is integration...so you can not evaluate about a point but an interval
the answers are the same. once you step outside the integration to use trig (modification). you are in algebra world hence the factor -1/48 as CAS showed
preval((1/48)*(-3*sin(2*x)^8+4*sin(2*x)^6),2,1)
preval((-1/16)*sin(2*x)^8+(1/12)*sin(2*x)^6-(1/48),2,1)
āˆ«(cos(2*x)^3*sin(2*x)^5,x,1,2)
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Messages In This Thread
Integrate question - DrD - 10-18-2017, 09:56 PM
RE: Integrate question - P_R_S - 10-18-2017, 10:29 PM
RE: Integrate question - DrD - 10-19-2017, 11:05 AM
RE: Integrate question - webmasterpdx - 10-19-2017, 02:27 AM
RE: Integrate question - DrD - 10-19-2017, 10:11 AM
RE: Integrate question - webmasterpdx - 10-19-2017, 10:42 AM
RE: Integrate question - webmasterpdx - 10-19-2017, 10:49 AM
RE: Integrate question - DrD - 10-19-2017, 11:23 AM
RE: Integrate question - webmasterpdx - 10-19-2017, 11:25 AM
RE: Integrate question - parisse - 10-19-2017, 12:00 PM
RE: Integrate question - webmasterpdx - 10-19-2017, 01:01 PM
RE: Integrate question - DrD - 10-19-2017, 01:26 PM
RE: Integrate question - parisse - 10-19-2017, 05:44 PM
RE: Integrate question - webmasterpdx - 10-19-2017, 02:12 PM
RE: Integrate question - DrD - 10-19-2017, 03:08 PM
RE: Integrate question - toshk - 10-19-2017 05:03 PM
RE: Integrate question - webmasterpdx - 10-19-2017, 07:34 PM
RE: Integrate question - roadrunner - 10-20-2017, 12:54 PM
RE: Integrate question - webmasterpdx - 10-20-2017, 02:50 PM
RE: Integrate question - DrD - 10-20-2017, 04:43 PM
RE: Integrate question - parisse - 10-20-2017, 05:58 PM
RE: Integrate question - DrD - 10-20-2017, 06:43 PM
RE: Integrate question - StephenG1CMZ - 10-21-2017, 06:59 AM
RE: Integrate question - DrD - 10-21-2017, 10:30 AM
RE: Integrate question - pier4r - 10-21-2017, 11:49 AM
RE: Integrate question - roadrunner - 10-20-2017, 04:53 PM
RE: Integrate question - toshk - 10-20-2017, 06:30 PM
RE: Integrate question - toshk - 10-20-2017, 07:05 PM
RE: Integrate question - webmasterpdx - 10-20-2017, 09:41 PM
RE: Integrate question - DrD - 10-20-2017, 10:41 PM
RE: Integrate question - Didier Lachieze - 10-21-2017, 04:29 AM
RE: Integrate question - webmasterpdx - 10-20-2017, 11:34 PM
RE: Integrate question - webmasterpdx - 10-21-2017, 04:53 AM
RE: Integrate question - Arno K - 10-21-2017, 07:03 AM
RE: Integrate question - webmasterpdx - 10-21-2017, 08:15 AM
RE: Integrate question - webmasterpdx - 10-21-2017, 11:02 AM



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