x_{min}

x_{max}

f(x)

Färbung a/b

sichtbar v

x

sichtbar u

Surface 1

1.Oberfläche:

►

- Aufbau

- Löschen

2. Gitternetz:

-f(x)

↹

$\scalebox{1.4} {Rotationsvolumen}$
$\scalebox{1.0}\text{ {  (Kurvenschichtung)} }$

$\scalebox{1.4} \text{\copyright Roman Chijner, Heidelberg 2012}$
    $\scalebox{1.3} \text{   Gestaltungshilfe: Werner Knobloch}$

f_x(u,v) = v

f_y(u,v) = f(v) \;sin(u)

f_z(u,v) = f(v)\;cos(u)

x_{min} = -5 (slider from -15 to 15, step 1)
P1: (x_{min}, 0)
x_{max} = 12 (slider from -5 to 15, step 1)
P2: (x_{max}, 0)
e = Segment(P1, P2)
a = 0.4 (slider from -5 to 5, step 0.1)
c = 10.4 (slider from -15 to 15, step 0.01)
b = 0.18 (slider from -5 to 5, step 0.01)
f = Function((((a * ℯ^(((-b) * x))) * cos(x)) * x) + c, x_{min}, x_{max})
Farbe = false
bv = true
Th = 1 (slider from 1 to 13, step 1)
bu = true
suf1 = false
fy(u, v) = (f(v) * sin(u))
Funktion = NaN (slider from 1 to 11, step 1)
fz(u, v) = (f(v) * cos(u))
fx(u, v) = v + (0 * u)
u_{max} = 6.283185307179586 (slider from -5 to 7, step 1)
u_{min} = 0 (slider from -5 to 5, step 1)
f3 = Surface(fx(u, v), fy(u, v), fz(u, v), u, u_{min}, u_{max}, v, x_{min}, x_{max})
NN = 40 (slider from 10 to 500, step 10)
f_1 = Mirror(f, xAxis)
A = Point(e)
d = OrthogonalLine(A, xAxis)
B = Intersect(f, d, (8.147935420922277, 10.182146057077354))
B' = Mirror(B, xAxis)
g = Segment(B', B)
P3: (x_{min}, f(x_{min}))
P3' = Mirror(P3, xAxis)
h = Segment(P3, P3')
P4: (x_{max}, f(x_{max}))
P4' = Mirror(P4, xAxis)
i = Segment(P4', P4)
j = IntegralBetween(f, (-f(x)), x_{min}, x_{max}, true)
c_1 = 0
c_2 = 0
P01: (x(A), 0, y(B))
k = Circle(xAxis, P01)
j1: (π * NIntegral[f(x)^(2), x_{min}, x_{max}])
text1: "V= π*\int_{x_{min} }^{x_{max} } f(x)^2*dx=" + (LaTeX[j1]) + "\;VE"
jh = false
text3: "$\scalebox{0.9}\text{Volumen des Rotationskörpers der}$
$\scalebox{0.9}\text{Funktion f(x) bei Rotation um die x-Achse$
$f(x)=" + (LaTeX[LaTeX[f, false]]) + "$"