Integrate question

[toshk]

(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 =−2.08333333333e−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)
∫(cos(2*x)^3*sin(2*x)^5,x,1,2)