Find Arc Length with TI-Nspire Calculator

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SUMMARY

The TI-Nspire calculator does not have a dedicated arc length function, but it can compute arc length using the integral formula: $\displaystyle \int_a^b{ \sqrt{ 1 + \left( \frac{\mathrm{d}y}{\mathrm{d}x} \right) ^2 } \, \mathrm{d}x }$. Users can utilize the integration function to find arc length by inputting the necessary parameters. While some users initially believed the arc length function would simplify the process, it ultimately requires the same input as the integral method. Programming options are available for TI calculators, allowing users to create custom functions for arc length calculations.

PREREQUISITES
  • Understanding of integral calculus, specifically arc length calculation.
  • Familiarity with the TI-Nspire calculator interface and functions.
  • Basic programming skills for TI calculators, particularly for creating custom functions.
  • Knowledge of differentiation to compute $\frac{\mathrm{d}y}{\mathrm{d}x}$ for the arc length formula.
NEXT STEPS
  • Learn how to use the TI-Nspire integration function for arc length calculations.
  • Explore programming capabilities on TI calculators to automate arc length computations.
  • Study integral calculus applications in real-world scenarios.
  • Investigate alternative graphing calculators that may offer dedicated arc length functions.
USEFUL FOR

Students, educators, and professionals in mathematics or engineering who require assistance with arc length calculations using the TI-Nspire calculator.

ineedhelpnow
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how do i use the nspire to find arc length?
 
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I don't think that there is an arclength function. But the formula for arclength is $\displaystyle \begin{align*} \int_a^b{ \sqrt{ 1 + \left( \frac{\mathrm{d}y}{\mathrm{d}x} \right) ^2 } \, \mathrm{d}x } \end{align*}$, and the TI N Spire does have the ability to solve integrals.
 
what i normally do is use the integration function but i noticed there was something for arc length and i figured it would be much easier (if i knew how to use it) using that instead of inputting the whole thing.

oh that's all it does? i thought all i had to was put in the original equation and it would solve. never mind then. function isn't as useful as i thought. thanks tho.
 
ineedhelpnow said:
what i normally do is use the integration function but i noticed there was something for arc length and i figured it would be much easier (if i knew how to use it) using that instead of inputting the whole thing.

oh that's all it does? i thought all i had to was put in the original equation and it would solve. never mind then. function isn't as useful as i thought. thanks tho.

I don't own one of those, but I own a TI-89 and have owned many TI graphing calculators in the past, and I am certain you could write a program that would prompt you for the limits and the function, and then would compute the arc length and then output the result. I used to love programming my calculators. :D
 
i used to have the ti-89 but i didnt really use it for anything besides simple stuff. once i got the ti-nspire, it was way easier because everything is already formatted. i think the best idea is to just use with the calculator offers me because I am pretty confident ill break it otherwise. :D
 

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