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 (CAS) Arc Leght Integral returning another integral
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(CAS) Arc Leght Integral returning another integral
08302016 09:16 AM
Hello!
I`m trying to solve the arc lenght of the function y(x)=2.5+9*xˆ20.5xˆ4, between the points x=0 and x=4.
The math to do that is to solve the inegral from 0 to 4 of sqrt(1+(18*x2*xˆ3)ˆ2) dx
The question is:
When I try to solve this particular integral, the calculator returns me another integral, in a recursive way, as if it can`t fully solve the first integral.
Does anybody know how to setup the calculator to be able to solve this kind of integral ?
My CAS setup is currently:
Angle: radians
Numeric format : Standard
Simplify: None
Exact [v]
Use sqrt [v]
Principal [v]
Recursive Evaluation: 10
Recursive Replacement: 2
Recursive Function: 20
Epsilon: 1E12
Probability: 1E15
Newton: 80
P.S: Wolfram Alpha does solve this kind of integral.
Solved! Go to Solution.
08302016 02:30 PM  edited 08302016 02:33 PM
Hello,
Luckily, there is no setup to do here!
Basically, you are asking the calculator to solve with a perfect, closed form which I'm not certain exists in this case. It runs for a while, and then when it can't make any more progress, returns the modified internal form "as close to the perfect, exact result" as it can. In this case, that is a square root value, and a modified integral.
Press Shift  ENTER to run the shifted ENTER function for an approximation on that result and the decimal answer pops out. That squiggly = sign is the mathematical sign for "approximates to".
Note that if you included a . in your initial entry, the approximate would immediately pop out as the CAS hits that apprixmate number and then continues in a "decimal approximation" form.
sqrt(1.+(18*x2*xˆ3)ˆ2) < note the . after the 1 indicates to the calculator "this is not a perfect, idea of 1 but rather an approximate number that is 1". That is a pretty big difference in mathematics.
If you put a 1. into your original input, it would immediately pop out the decimal. However, just using the Shift ENTER key as needed is generally the simplest way to do it.
Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
08302016 05:30 PM  last edited on 05172019 09:38 AM by WanderP
Hi!, @luiz_aug:
See, this image, for comparison between Wolfram Alpha and HP PRIME (exact and approximate) ....
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
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