Rechteck

b = %v

a = %v

exp

Rechteck

exp

b = %v

a = %v

$f_2(t-x)$

$f_1(x) * f_2(t-x)$

$\int_{-\infty}^{\infty} (f_1(x) \cdot f_2(t-x))dx$

$f_1(x)$

$f_2(x)$

f_1

f_2

a:

b:

a:

b:

f1Rectangle = false
b2 = 2.75 (slider from -5 to 5)
a2 = 1.25 (slider from -5 to 5)
f2Exp = false
e(x) = If[x > 0, ℯ^((-x)), 0]
rect(x, a, b) = (((0.5 * sgn(x - a)) + 0.5) * ((-0.5 * sgn(x - b)) + 0.5))
rect2(a, b, x) = If[a < x < b, 1, 0]
f2Rectangle = true
f1Exp = true
b1 = 3 (slider from -5 to 5)
a1 = 0.5 (slider from -5 to 5)
t = 1 (slider from -2.5 to 10, step 0.01)
area_{rect} = If(t - a2 > a1 ∧ t - b2 < b1, Min[t - a2, b1] - Max[t - b2, a1], 0)
f_1 = If(f1Exp ≟ 1, e, If[f2Rectangle ≟ 1, rect2(a1, b1, x), rect(x, a1, b1)])
f_2 = If(f2Exp ≟ 1, e, If[f1Rectangle ≟ 1, rect2(a2, b2, x), rect(x, a2, b2)])
f_3(x) = f_2(t - x)
p = Simplify((f_1(x) * f_3(x)))
area = If(f1Rectangle ∧ f2Rectangle, area_{rect}, Integral[p, -10, 10])
P_t: (t, area)
g_1(x) = f_1(x) + 0.01
g_2(x) = f_2(x) - 0.01
f1a = Textfield(a1)
f1b = Textfield(b1)
f2a = Textfield(a2)
f2b = Textfield(b2)
vertLines_{f3}: {Segment[(t - b2, 0), (t - b2, 1)], Segment[(t - a2, 0), (t - a2, 1)]}
vertLines_{f1}: {Segment[(a1, 0), (a1, 1)], Segment[(b1, 0), (b1, 1)]}
vertLines_{f2}: {Segment[(a2, 0), (a2, 1 - 0.01)], Segment[(b2, 0), (b2, 1 - 0.01)]}
clearTraceHandlePosition = (0, 0)
area_{Visual}(x, y) = 0 < y < p(x)