a

b

f(x)=sen x

x

F(x)=\int_{a}^{x} f(t)\,dt\

F'(x)=\
\displaystyle \lim_{h \to 0}\dfrac{\int_{a}^{x+h} f(t)\,dt-\int_{a}^{x} f(t)\,dt}{h}=

x+h

\lim_{h \to 0}\dfrac{\int_{a}^{x+h} f(t)\,dt+\int_{x}^{a} f(t)\,dt}{h}=\
\lim_{h \to 0}\dfrac{\int_{x}^{x+h} f(t)\,dt}{h}=

c

f(c)

\\lim_{h \to 0}\dfrac{f(c)·(x+h-x)}{h}=

\\lim_{h \to 0} f(c)=

f(x)

f(x)

Lleva h hasta cero

F'(x)=f(x)

a = 0.3306142382167716
P_a: (a, 0)
P_b = Point(xAxis)
f(x) = sin(x)
hh = 1 (slider from -5 to 5, step 0.1)
P_x = Point(xAxis)
A_{x} = Integral(f, a, x(P_x))
P_{xh}: (x(P_x) + hh, 0)
g = Invert(f)
A_{xblanco} = Integral(f, a, x(P_x))
A_{x+h} = Integral(f, a, x(P_{xh}))
area: A_{x+h} - A_{x}
cc: g(area / hh)
r_1 = OrthogonalLine(P_x, xAxis)
A_{xblanco2} = Integral(f, a, x(P_x))
j = Segment(P_a, P_x)
A_h = Integral(f, x(P_x), x(P_{xh}))
c = If(cc > x(P_x), g(area / hh), π - g(area / hh))
P_c: (c, 0)
R: (0, f(c))
C: (c, f(c))
r_2 = OrthogonalLine(P_{xh}, xAxis)
r_3 = OrthogonalLine(C, r_1)
E = Intersect(r_2, r_3)
F = Intersect(r_1, r_3)
polígono1, s_3, s_2, s_1, s_4 = Polygon(F, P_x, P_{xh}, E)
X = Intersect(f, r_1, (0.7078497293290353, 0.6502015820486619))
Q: (0, f(x(P_x)))
h = 1 (slider from 0 to 1, step 0.1)
k = Segment(Q, X)
i = Segment(X, P_x)