Casio fx-991CW and TI-30X Pro MathPrint: Arc Length of f(x)
Here is a tip for calculus class.
Calculating The Arc Length of f(x)
The arc length of f(x) is defined as:
∫( √( 1 + (f'(x))^2 ) dx, x = a to x = b)
With the two function memory, f(x) and g(x), on the Casio fx-991CW and TI-30X Pro MathPrint, we can calculate arc length with the expression:
∫( √( 1 + (g(x))^2 ) dx, x = a to x = b)
where g(x) = d/dx f(x)
Setup Instructions
Casio fx-991CW
To set up f(x) and g(x):
1. Press [ f(x) ], select Define f(x) to define the function. Press [ EXE ] to register it.
2. Press [ f(x) ], select Define g(x) to define the derivative. Press [ EXE ] to register it.
3. Recall f(x) and g(x) by pressing [ f(x) ] and selecting the function.
Derivative:
g(x) = ( (f(x + h) - f(x) )/h [h is sufficiently small, like 0.001]
The integral function on the fx-991CW does not allow to have the derivative command in the integrand. Therefore, the definition of the derivative must be used.
TI-30X Pro MathPrint
To set up f(x) and g(x):
1. Press [ table ]. Select Add/Edict Func.
2. Edit f(x), then press [ enter ].
3. Edit g(x), enter the derivative. Press [ enter ].
4. Press [ 2nd ] (quit) to exit Table mode.
5. Recall f(x) and g(x) by pressing [ table ] and selecting the function.
Derivative:
g(x) = ( (f(x + h) - f(x) )/h [h is sufficiently small, like 0.001]
or
g(x) = d/dx( f(x) )|x=x
Note: The TI-30X Pro MathPrint is a European version of the TI-36X Pro. The TI-36X Pro has only one function memory slot.
In any calculus problem, set the angle mode to Radians.
Examples
1. f(x) = x^3 + 1 from x = 0 to x = 3.
For this first example, screens are from the Casio fx-991CW.
Arc length ≈ 27.65808204
2. f(x) = sin x from x = 0 to x = π
Arc length ≈ 3.820197739
3. f(x) = 4x^2 + 1 from x = 0 to x = 1
Arc length ≈ 1.478942858
Eddie
All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
