$ y=x^2 $のグラフの０から１までの面積を求めるとき

０から１を$\frac{1}{n}$ずつ区切って次のように面積をだしてみよう．

$ x=\frac{1}{n} $のときのグラフのｙ座標を高さとし，四角形の面積を求める．

ｎ＝１のとき

面積は？

省略

ｎ＝２のとき

ｎ＝４のとき

面積は？

ｎ＝１０のとき

面積は？

このように

結果

少しずつグラフの面積に近づいていく

nを∞にすることによりグラフの面積にほど近くなる．

よって

これを区分求積法という．

b = 0 (slider from 0 to 1, step 1)
A = (1.0018889337121737, 4.7480036419684027E-4)
B = (1.0032684769272404, 0.5647079753265016)
C = (0.5, 0.25)
D = (1, 1)
E = (0.5, 1)
F = (0, 0.25)
d = Segment(F, C)
e = Segment(C, E)
f = Segment(E, D)
G = Point(xAxis)
g = Segment(C, G)
多角形1, e_1, d_1, a_1, g_1 = Polygon(E, D, A, G)
H = Intersect(c, xAxis, 1)
多角形2, f_1, c_1, g_2, h = Polygon(F, C, G, H)
a = 0 (slider from 0 to 1, step 1)
I = (1, 1)
J = Intersect(a_1, xAxis)
K = (0.7480529821398898, -9.047428508699199E-4)
L = (0.2472787950706558, -9.047428508699199E-4)
M = (0.25, 0.0625)
N = (0, 0.0625)
O = (0.25, 0.25)
P = (0.75, 0.5625)
Q = (0.75, 1)
R = (0.5, 0.5625)
多角形3, q, i, a_2, k = Polygon(Q, I, A, K)
多角形4, p, r, j, k_1 = Polygon(P, R, J, K)
S = Intersect(c, r, 1)
多角形5, o, s, j_1, l = Polygon(O, S, J, L)
多角形6, m, n, h_1, l_1 = Polygon(M, N, H, L)
t = 0 (slider from 0 to 1, step 1)
T = (0.1, 0)
U = (0.2, 0)
V = (0.3, 0)
W = (0.4, 0)
Z = (0.5, 0)
A_1 = (0.6, 0)
B_1 = (0.7, 0)
C_1 = (0.8, 0)
D_1 = (0.9, 0)
F_1 = (0.14933122680091582, 4.7480036419683984E-4)
T1 = (0.1, 0.01)
T2 = (0, 0.01)
U1 = (0.2, 0.04)
U2 = (0.1, 0.04)
V1 = (0.3, 0.09)
V2 = (0.2, 0.09)
W1 = (0.4, 0.16)
W2 = (0.3, 0.16)
Z1 = (0.5, 0.25)
Z2 = (0.4, 0.25)
A11 = (0.6, 0.36)
A12 = (0.5, 0.36)
B11 = (0.7, 0.49)
B12 = (0.6, 0.49)
C11 = (0.8, 0.64)
C12 = (0.7, 0.64)
D11 = (0.9, 0.81)
D12 = (0.8, 0.81)
D13 = (1, 1)
D14 = (0.9, 1)
多角形7, d13, d14, d_2, a_3 = Polygon(D13, D14, D_1, A)
多角形8, d11, d12, c_2, d_3 = Polygon(D11, D12, C_1, D_1)
多角形9, c11, c12, b_1, c_3 = Polygon(C11, C12, B_1, C_1)
多角形10, b11, b12, a_4, b_2 = Polygon(B11, B12, A_1, B_1)
多角形11, a11, a12, z, a_5 = Polygon(A11, A12, Z, A_1)
多角形12, z1, z2, w, z_1 = Polygon(Z1, Z2, W, Z)
多角形13, w1, w2, v, w_1 = Polygon(W1, W2, V, W)
多角形14, v1, v2, u, v_1 = Polygon(V1, V2, U, V)
多角形15, u1, u2, t_1, u_1 = Polygon(U1, U2, T, U)
多角形16, t1, t2, h_2, t_2 = Polygon(T1, T2, H, T)
多角形17, b11_1, b_3, a_6, b12_1 = Polygon(B11, B_1, A_1, B12)
α = 0 (slider from 0 to 1, step 1)
i_1 = 0 (slider from 0 to 1, step 1)