Solving definite integral

[celltx]

Scott Collins posted a Youtube video on solving a definite integral. To some degree, this reflects my own personal experience dealing with various Prime inconsistencies:

https://www.youtube.com/watch?v=8Snx7OmMmCg

[Wes Loewer]

There were three issues that he was dealing with here.

1) The issue that he solved by using parentheses was actually a result of putting X=5 in the dX field. This is easy to accidentally do and I tell my students to be sure to use the right arrow key to move out of the dX field. You can see the difference when you enter the expression, but, unfortunately, whether entered correctly or incorrectly, both are displayed the same afterwards. So even though he entered the expression incorrectly, it is easy to see how this could be done and the calculator gives no meaningful indication of what is wrong. (There was a thread here about this issue, but I can't seem to find it right now.)

2) When using an initial guess of 1000, his calculator locked up. On my calculator (firmware 2021-12-02) it does not lock up, but it does take about 18 seconds to find the solution. While waiting, I was able to stop the calculation by holding the ON button. I'm not sure why his locked up, but sometimes things go wrong and that's why the Prime, Nspire, 84+CE all put a reset buttons on the back (since you can't pull a battery anymore). ON-C would have also done the trick.

3) He kept entering 1.5*pi and getting 4.71238898038 which he kept saying was wrong, but this is correct. Likewise, 1.5*3.14 really is 4.71. I gather that he wanted a literal '1.5*pi' in the initial guess box, but for a numerical solver, it is not unreasonable to require a number. Using the CAS solver, solve(∫(sqrt(sin(X)^2+1),X,0,a) = 5,a = 1.5*π) does what he wanted.

In each of these three cases, you could argue that he did something wrong, but if a user can't figure out how to do it right, then there needs to be some changes in the interface.

1) The dX matter is a long-standing issue that needs addressing. The Nspire puts parentheses around anything that is more than a variable, so it would look like d(X=5) which the user would immediately recognize as being incorrect.

3) Maybe the numeric solver should allow literal expressions placed in single quotes. This could be evaluated internally before the solving process starts. (The user would still need to know how to use the ' ' quotes, but that's another matter.)

[Wes Loewer]

(02-07-2022 04:45 PM)Wes Loewer Wrote:  (There was a thread here about this issue, but I can't seem to find it right now.)

Found it: https://www.hpmuseum.org/forum/thread-17272.html