Integrate question

[Didier Lachieze]

(10-20-2017 10:41 PM)DrD Wrote:  

(10-20-2017 09:41 PM)webmasterpdx Wrote:  Note that neither answer is "less accurate" than the other.

Totally disagree. A single specified constant is less accurate, because a whole family of constants are allowable. To restrict the result to just the one value, is to ignore all the others including 0. The proof is the comparison between hand / similar technologies, when compared with CAS/xcas. Just focus on the difference, which is NOT 0.

Hi DrD, I've followed this discussion with a great interest because I've always found such discussions on the hpmuseum forum are a great way to learn from great people and I'm learning everyday.
However, with my limited math capabilities I don't understand how the difference can tell you that one of the two operand is more restricted than the other, or that one is more accurate.

The Prime CAS returns a result expressed with cos functions, the hand method a result expressed with sin functions ;
CAS : (-3*cos(2*x)^8+8*cos(2*x)^6-6*cos(2*x)^4)/48
Hand: -(3*sin(2*x)^8-4*sin(2*x)^6)/48

Both are correct and none includes an explicit constant.
If you rewrite the CAS result to use sin functions you will get :
CAS = Hand -1/48

But you can also choose to rewrite the Hand result to use cos functions and then you get:
Hand = CAS +1/48

This doesn't tell anything about one solution being more accurate or less restrictive than the other.

Unless there is an elephant in the room... an assumption that was not explicitly stated: that the CAS should use the Hand method to get a matching result. But here there is not a single method to get a mathematical valid result and without explicitly telling to the CAS (either by design or as a parameter) which method you want it to use, I don't see how you can complain about the CAS result.

Personally, if I were expecting a student to solve by hand an indefinite integral, I would also expect him to be smart enough to understand what an indefinite integral is and that two solutions differing only by a constant are both equally valid. Your expectations may be different, and you may want a CAS tailored to a given textbook to provide literally the same results.

This may be due to the difference in how maths are teached in the U.S. and in France and may (or may not...) explain partially why with 1/5th of the population, France has almost the same number of Fields medals than the U.S.: List of countries by number of Fields Medallists.
This being said without any intention to launch a flame war, education in France is far from perfection and it's always good to look how things are done elsewhere to get good ideas for improvement.