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
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