Parempoolne integraal

Vasakpoolne integraal

Trapetsvalemiga integraal

y = a x² - 5a x + 4a

Tegelik \;  integraali  \; väärtus \;  on  \; -\frac{5}{6}

Integraali 0-st 5-ni arvutamine joonise abil

Ehk nende valemite abil on küll jooniselt lihtne arvutada,
kuid sisse tekib väike viga

Tegelik integraal

a = 3 (slider from 1 to 5, step 1)
F: y = (a * x^(2)) - ((5 * a) * x) + (4 * a)
A: (1, F(1))
B: (2, F(2))
C: (3, F(3))
D: (4, F(4))
Y = Point(xAxis)
Z = Point(xAxis)
X = Intersect(xAxis, yAxis)
W = Point(xAxis)
E: (0, F(0))
G: (5, F(5))
hulknurk1, x_1, e, a_1, b, c, d, g, w = Polygon(X, E, A, B, C, D, G, W)
f = Segment(Y, B)
h = Segment(Z, C)
A_1: (1, F(0))
B_1: (2, F(1))
C_1: (3, F(2))
D_1: (4, F(3))
E_1: (5, F(4))
hulknurk2, x_2, e_1, i, a_2, b_1, b_2, c_1, d_1, d_2, j = Polygon(X, E, A_1, A, B_1, B, C_1, D_1, D, E_1)
k = Segment(Z, C)
A_2: (1, F(2))
B_2: (2, F(3))
C_2: (3, F(4))
D_2: (4, F(5))
hulknurk3, x_3, a_3, l, m, c_2, n, d_3, p, g_1, w_1 = Polygon(X, A, A_2, B_2, C, C_2, D, D_2, G, W)
q = Segment(Y, B)
Punkthulknurk1 = PointIn(hulknurk1)
Punkthulknurk2 = PointIn(hulknurk2)
Punkthulknurk3 = PointIn(hulknurk3)
o = false
r = false
s = false
q1, a_4, t, c_3, z_1 = Polygon(A, A_2, C, Z)
q2, d_4, w_2, g_2, f_1 = Polygon(D, W, G, D_2)
i_1: q2 - q1
tekst1: "Parempoolse integraali valemi järgi on integraal " + i_1 + ""
tekst2: "Vasakpoolse integraali valemi järgi on integraal " + i_1 + ""
t1, a_5, e_2, x_4 = Polygon(E, X, A)
q3, a_6, b_3, c_4, d_5 = Polygon(A, B, C, D)
i_2: (2 * t1) - q3
tekst3: "Trapetsvalemi järgi on integraal " + i_2 + ""
u = false