曲線下的面積(1)
Author: 藍邦偉  老師

R_1

R_2

A_1

A_2

A_3

A_4

A

B

C

積分與曲線下的面積

y=f(x)

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.76 * Corner[1] + 0.24 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
A_1 = (-1.7055473878180403, -0.6667815980033079)
A_2 = (1.76075623145421, 1.3919926728371772)
A_3 = (3.8615463037404223, -0.9188764066776518)
A_4 = (7, 1)
f_1 = Polynomial({A_1, A_2, A_3, A_4})
P_1, P_2, P_3 = Intersect(f_1, xAxis)
a = Integral(f_1, x(P_1), x(P_2))
b = Integral(f_1, x(P_2), x(P_3))
I_1: "$R_1=\int_{" + (LaTeX[x(P_1)]) + "}^{" + (LaTeX[x(P_2)]) + "}{f(x)dx }$
       $=" + (LaTeX[a]) + "$"
I: "$R=|R_1|+|R_2|$
     $=" + (LaTeX[abs(a)]) + "+" + (LaTeX[abs(b)]) + "=" + (LaTeX[abs(a) + abs(b)]) + "$"
I_3: "$ R_2=\int_{" + (LaTeX[x(P_2)]) + "}^{" + (LaTeX[x(P_3)]) + "}{ f(x)dx}$
      $=" + (LaTeX[b]) + "$"