You wrote
> Recently I had occasion to try to integrate x^(n+1) on the TI-92 in a context
> where n could be any number greater than 1. The calculator refuses to do it
> though it will integrate x^n without hesitation. A quirk of the software, no
> doubt.
Interesting. I don't have the '92 but DeriveXM produces
antiderivativesint(x^n,x) = (x^(n+1)-1)/(n+1)
int(x^(n+1),x) = (x^(n+2)-1)/(n+2)
indicating that it's assuming a lower bound of integration = 1. This is perhaps
an attempt to be consistent with the definition ln(x) = int(1/t,t,1,x)
> Also, I have found that even very simple definite integrals can take an
> incredibly long time. If you're not familiar with this behavior, try
> integrating
>
> x^6 - 2x^5 + x^4 + 3x^3 - 4x^2 + x - 5
>
> with limits of 0 and 1.
DeriveXM spits this out in 0.1 seconds =1/4 of a thumb twiddle.
This may also explain the difficulty with sin(ln(x)); that is, it is assuming
some lower bound (constant of integration) - if the lower bound were close to 0,
then the integral is divergent. The question is then what does it use for the
lower bound?
Geoff H
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