Montrer les trapèzes

Montrer les rectangles inférieurs

Montrer les rectangles supérieurs

f(x) = 0.5 x^(2)
A = Point(xAxis)
B = Point(xAxis)
n = 2 (slider from 0 to 30, step 1)
l: x(B) - x(A)
L1 = Sequence(Segment[(x(A) + i l / n, f(x(A) + i l / n)), (x(A) + (i + 1) l / n, f(x(A) + (i + 1) l / n))], i, 0, n - 1)
L3 = Sequence(Polygon[(x(A) + i l / n, 0), (x(A) + i l / n, f(x(A) + i l / n)), (x(A) + (i + 1) l / n, f(x(A) + (i + 1) l / n)), (x(A) + (i + 1) l / n, 0)], i, 0, n - 1)
L2 = Sequence(Segment[(x(A) + i l / n, 0), (x(A) + i l / n, f(x(A) + i l / n))], i, 0, n)
RI = LowerSum(f, x(A), x(B), n)
RS = UpperSum(f, x(A), x(B), n)
T2: "Aire des rectangles supérieurs=" + RS
s: {1.619405849108368, 4.4697502331961605}
L4 = Sequence(Area[(x(A) + i l / n, 0), (x(A) + i l / n, f(x(A) + i l / n)), (x(A) + (i + 1) l / n, f(x(A) + (i + 1) l / n)), (x(A) + (i + 1) l / n, 0)], i, 0, n - 1)
T = Somme(L4)
T3: "Aire des trapèzes=" + T
a = true
T1: "Aire des rectangles inférieurs=" + RI
b = false
c = false
C: (x(A), f(x(A)))
D: (x(B), f(x(B)))
d = Segment(A, C)
e = Segment(D, B)

Tool: Somme
Liste: ajoute tous les nombres d'une liste
Input: L1
Output: a

L1: {1.619405849108368, 4.4697502331961605}
L2 = Sequence(If[i ≤ Length[L1], Element[L1, i], 0] + If[i + 1 ≤ Length[L1], Element[L1, i + 1], 0] + If[i + 2 ≤ Length[L1], Element[L1, i + 2], 0] + If[i + 3 ≤ Length[L1], Element[L1, i + 3], 0] + If[i + 4 ≤ Length[L1], Element[L1, i + 4], 0] + If[i + 5 ≤ Length[L1], Element[L1, i + 5], 0] + If[i + 6 ≤ Length[L1], Element[L1, i + 6] + If[i + 7 ≤ Length[L1], Element[L1, i + 7], 0] + If[i + 8 ≤ Length[L1], Element[L1, i + 8], 0], 0] + If[i + 9 ≤ Length[L1], Element[L1, i + 9], 0], i, 1, Length[L1], 10)
L3 = Sequence(If[i ≤ Length[L2], Element[L2, i], 0] + If[i + 1 ≤ Length[L2], Element[L2, i + 1], 0] + If[i + 2 ≤ Length[L2], Element[L2, i + 2], 0] + If[i + 3 ≤ Length[L2], Element[L2, i + 3], 0] + If[i + 4 ≤ Length[L2], Element[L2, i + 4], 0] + If[i + 5 ≤ Length[L2], Element[L2, i + 5], 0] + If[i + 6 ≤ Length[L2], Element[L2, i + 6] + If[i + 7 ≤ Length[L2], Element[L2, i + 7], 0] + If[i + 8 ≤ Length[L2], Element[L2, i + 8], 0], 0] + If[i + 9 ≤ Length[L2], Element[L2, i + 9], 0], i, 1, Length[L2], 10)
L4 = Sequence(If[i ≤ Length[L3], Element[L3, i], 0] + If[i + 1 ≤ Length[L3], Element[L3, i + 1], 0] + If[i + 2 ≤ Length[L3], Element[L3, i + 2], 0] + If[i + 3 ≤ Length[L3], Element[L3, i + 3], 0] + If[i + 4 ≤ Length[L3], Element[L3, i + 4], 0] + If[i + 5 ≤ Length[L3], Element[L3, i + 5], 0] + If[i + 6 ≤ Length[L3], Element[L3, i + 6] + If[i + 7 ≤ Length[L3], Element[L3, i + 7], 0] + If[i + 8 ≤ Length[L3], Element[L3, i + 8], 0], 0] + If[i + 9 ≤ Length[L3], Element[L3, i + 9], 0], i, 1, Length[L3], 10)
L5 = Sequence(If[i ≤ Length[L4], Element[L4, i], 0] + If[i + 1 ≤ Length[L4], Element[L4, i + 1], 0] + If[i + 2 ≤ Length[L4], Element[L4, i + 2], 0] + If[i + 3 ≤ Length[L4], Element[L4, i + 3], 0] + If[i + 4 ≤ Length[L4], Element[L4, i + 4], 0] + If[i + 5 ≤ Length[L4], Element[L4, i + 5], 0] + If[i + 6 ≤ Length[L4], Element[L4, i + 6] + If[i + 7 ≤ Length[L4], Element[L4, i + 7], 0] + If[i + 8 ≤ Length[L4], Element[L4, i + 8], 0], 0] + If[i + 9 ≤ Length[L4], Element[L4, i + 9], 0], i, 1, Length[L4], 10)
a = Element(L5, 1)