Area Under the Curve Using Parametric Curves: Casio Classpad fx-CP400 and HP Prime (CAS)
The CAS (computer algebra system) function paramint
calculates the area under the curve of a function defined as the parametric
curve (x(t), y(t)). The integral is ∫ y(t) * x’(t) dt .
Casio Classpad fx-CP400:
paramint
It would the most efficient way is use the Define command on
the home screen (like the screen shot above).
Define paramint(xt,yt,t0,t1) = ∫ (yt * diff(xt,t) dt, t = t0
to t = t1)
HP Prime:
paramint (CAS Program)
The program paramint is going to be defined as CAS function. When first creating paramint, check the CAS
box before pressing the soft key (OK).
Also pay attention to the letters being typed while using the ALPHA
key. In the program editor, letters are
defaulted to uppercase while CAS variables are lowercase. Finally, commands called from the Toolbox in
Program editing mode will have a “CAS.” suffix.
Erase the suffices.
#cas
paramint(xt,yt,t0,t1):=
BEGIN
LOCAL
n;
n:=int(yt*diff(xt,t),t,t0,t1);
return
n;
END;
#end
Examples
Example 1: x(t) =
2t^3 + 1, y(t) = t^2, t0 = 0, t1 = 1
Result: 6/5
Example 2: x(t) = sin
t, y(t) = 3 cos t, t0 = 0, t1 = π
Result: 3/2*π ≈ 4.71238898039
This blog is property of Edward Shore, 2016
