Choose a function f(x) =

Choose a value for b =

Define A(x) by choosing a lower limit for the integral =

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Strt = 2
f(x) = x + 3 * sin(x)
Δx = 0.51 (slider from -1 to 1, step 0.01)
b = 6
Aofb = Integral(f, Strt, b)
a: b + Δx
Aofa = Integral(f, Strt, a)
fx = Textfield(f)
b1_1 = Textfield()
approx: (Aofa - Aofb) / Δx
b1 = Textfield(b)
fofb: f(b)
c = 2
St = Textfield(Strt)
text3: "$" + (LaTeX[fofb]) + "=f(" + (LaTeX[b]) + ") $"
text1: "Approximate $\mathcal{A'(b)}$ for$\mathcal{ \; A}(x)=\int_{" + (LaTeX[Strt]) + "}^{x}{f(x)dx }"
text2: "$ \mathcal{A}'(" + (LaTeX[b]) + ")≈\frac{\mathcal{A}(" + (LaTeX[b]) + "+\Delta x)-\mathcal{A}(" + (LaTeX[b]) + ")}{\Delta x}=\frac{\int_{" + (LaTeX[Strt]) + "}^{" + (LaTeX[a]) + "}{(" + (LaTeX[f]) + ") dx \; -\int_{" + (LaTeX[Strt]) + "}^{" + (LaTeX[b]) + "}{(" + (LaTeX[f]) + ")dx }}}{" + (LaTeX[a]) + " \; -" + (LaTeX[b]) + "}="
text4: "$= \frac{" + (LaTeX[Aofa]) + " - " + (LaTeX[Aofb]) + "}{" + (LaTeX[Δx]) + " }= " + (LaTeX[approx]) + "$"
e = Line((0, approx), (b, approx))
A = Intersect(f, e, (6.255228387219166, 6.171368552326733))
d = Segment((0, approx), A)
Integrals = true
poly1, h, i, j, k = Polygon((b, 0), (b, approx), (a, approx), (a, 0))
fofa: f(a)
n = Segment((b, 0), (b, fofb))
m = Segment((a, 0), (a, fofa))
l = true