f(x)\; =\; 0.018\,x^3\:-\:0.018\,x^2\:-\:0.281\,x\;+\:0.281

G_g

G_f

f(x) = g(x)

a = -4 (slider from -4 to 4, step 0.1)
b = 4 (slider from -4 to 4, step 0.1)
c = 3.5 (slider from 1 to 10, step 0.5)
f = Function(1.5 c * (x + 4) * (x - 4) * (x - 1) / 85.33, -4.5, 4.5)
c_1 = Integral(f, a, b)
A: (a, f(a))
B: (a, 0)
C: (b, f(b))
D: (b, 0)
text1: "\\int_{a }^{b }  = " + c_1
text2: "\int_{" + a + "}^{" + b + "}\;" + c + "\;\cdot\;f(x)dx \;=\; " + c_1
text3: "\int_{" + a + "}^{" + b + "} f(x)dx \;=\; " + c_1
f' = Derivative(f)
g = Integral(f')
h(x) = g(x) + 24 c / 85.33
d = 0.2812609867572952
text4: "g(x) \;=\;" + c + "\;\cdot\; (0.018\,x^3\:-\:0.018\,x^2\:-\:0.281\,x\;+\:0.281)"
Text: (-1.2, f(-1.2))
p = Function(f(x) / c, -4.5, 4.5)
E: (-3.2, p(-3.2))