[CAS] Integrals

[DrD]

(09-28-2017 05:14 AM)parisse Wrote:  Make a graph and compute the area under the curve. For 1/x^2 (or even powers), all the area is positive, you get an infinite area. For 1/x, the discussion is more open, you can argue it is 0 or leave it undefined.
And don't forget that a CAS just does computation, you must use your brain to interpret the answer.

For an area under the curve to exist, 1/x^n must exist. This is where the confusion between my brain and CAS are conflicting. Specifically, there is a continuous interval, [-1,1], which includes x=0. So analytical approaches, such as graphing, are merely warning that the area is not continuous at 0. The result should be undef, for all 1/x^n, where x=0.

Wolfram agrees. Try plotting Y=int(1/X^2,X,-1,1) in the Advanced Graphing App. It, too, seems to agree with Wolfram. CAS reports an infinite area, which is less accurate than an undefined area.

If painting a curvy chateau is the task, and part of the area doesn't exist, (perhaps due to a partition), CAS is saying an infinite amount of paint must be purchased to complete the task, and you'll need the rest of your life, (and any reincarnations), to accomplish it. (If that area is modeled by an even power of 1/x^n, at x=0). So much for technology!