Initialize

i

f(z)=

magnify

number of section

Sequence(t-sin(t) +i*(1-cos(t)) ,t,0,2pi,delta)

section1

n

 Sequence(t+i*t*(t-2pi)/4,t,2pi,0,-delta )

section2

delta = 0.2 (slider from 0.01 to 0.5, step 0.01)
xpts2 = Sequence(t + ((ί * t) * (t - (2 * π)) / 4), t, (2 * π), 0, (-delta))
xpts1 = Sequence(t - sin(t) + (ί * (1 - cos(t))), t, 0, (2 * π), delta)
NK6 = NaN
KC6 = NaN
xptsall = Flatten({xpts1, xpts2})
InputBox1 = Textfield(xfunc)
xk = 1.98 (slider from 0.01 to 5, step 0.01)
xcnum = 2 (slider from 1 to 10, step 1)
xsection1 = Textfield(xptstxt1)
xpts = Remove(xptsall, Last[xptsall])
xpnum = Length(xpts)
xtxt1: "division=" + xpnum + ""
xn = 1 (slider from 1 to xpnum, step 1)
xmaxsection = 2
xfz = Zip(ί, z, xpts)
xdz = Sequence(Vector[Element[xptsall, k], Element[xptsall, k + 1]], k, 1, xpnum)
xvf = Zip(Vector[p, p + (xk * q)], p, xpts, q, xfz)
xfdz = Zip((ToComplex[a] * ToComplex[b]), a, xfz, Vector[b], xdz)
xfoots = Append((0, 0), Sequence[Sum[xfdz, k], k, 1, xpnum])
xsumvf = Zip(Vector[p, p + q], p, xfoots, q, Take[xfdz, 1, xn])
xtotal = ToComplex(Element[xfoots, xn + 1])
xdzk = Element(xdz, xn)
xvfk = Element(xvf, xn)
xsumvfk = Element(xsumvf, xn)
xtxt2: "\sum_{k=1}^{" + (LaTeX[xn]) + "}f(z_k)(z_{k+1}-z_k)\\
\ = " + (LaTeX[xtotal]) + ""
xptstxts = Sequence("xptstxt" + (k), k, 1, xcnum)
xptsnames = Sequence("xpts" + (k), k, 1, xcnum)
xsection2 = Textfield(xptstxt2)

Tool: mkptsonarc
mkptsonarc[ <Point>, <Circle>, <Point>, <Number>, <Number> ]
Input: A, c, B, delta, M
Output: ptsonarc

D = Center(c)
Na: ceil(c / delta)
Narc: (1 / 2 * (Na - M - abs(Na - M))) + M
ptsonarc = If(Defined[Intersect[c, ((A - D) * ℯ^((ί * Angle[A, D, B] / 2))) + D]], Sequence[((A - D) * ℯ^(((ί * k) * Angle[A, D, B] / Narc))) + D, k, 0, Narc - 1], Sequence[((A - D) * ℯ^((((-ί) * k) * Angle[B, D, A] / Narc))) + D, k, 0, Narc - 1])

Tool: mkptsonseg
mkptsonseg[ <Point>, <Point>, <Number>, <Number> ]
Input: A, B, delta, M
Output: ptsonseg

f = Segment(A, B)
Ns: ceil(f / delta)
N: (1 / 2 * (Ns - M - abs(Ns - M))) + M
ptsonseg = Sequence(((1 - k / N) * ToComplex[A]) + (k / N * ToComplex[B]), k, 0, N - 1)