x

y

%x

A = (0, -4)
B = (0, 4)
curvehFull = CircleArc((0, 0), A, B)
curvegFull = CircleArc((0, 0), B, A)
ymin = -6.2341536039552645
ymax = 4.9437515503746186
threshold = 0.03
xmax = 7.278520430924345
xmin = -6.838701345804035
xlabeldisplayed: "" + (LaTeX[xlabel]) + ""
ylabeldisplayed: "" + (LaTeX[ylabel]) + ""
nv = 9
vecfraction = 0.9
dxvec: ((xmax - xmin) * vecfraction / (nv - 1))
vecposX: xmin + ((0.5 * (1 - vecfraction)) * (xmax - xmin)) + (Sequence[i, i, 0, nv - 1] * dxvec)
dyvec: ((ymax - ymin) * vecfraction / (nv - 1))
vecposY: ymin + ((0.5 * (1 - vecfraction)) * (ymax - ymin)) + (Sequence[i, i, 0, nv - 1] * dyvec)
vecmag = 0.1
curvefFull = Segment(A, B)
f(t) = 0
g(t) = (-sqrt(16 - t^(2)))
h(t) = sqrt(16 - t^(2))
D = Point(curvegFull)
E = Point(curvehFull)
C = Point(curvefFull)
curvefPart = Segment(A, C)
fintf(t) = 0
intf: fintf(y(C))
fintg(t) = (8 * (π + ((2 * sgn(t)) * asin(abs(t) / 4))))
intg: fintg(y(D))
finth(t) = (-8 * (π + ((2 * sgn(t)) * asin(abs(t) / 4))))
inth: finth(y(E))
all_integrals: "\begin{align*}\dlint &= " + intf + "\\\lint{\adlc}{\dlvf} &=" + intg + "\\ \lint{\sadlc}{\dlvf} &= " + inth + "\end{align*}"
slidery = -5
a: y = slidery
sliderdy = 0.1
sliderdx = 1
list1 = Sequence(Segment[(i, slidery - sliderdy), (i, slidery + sliderdy)], i, -6, 6, sliderdx)
vecfield = Sequence(Sequence[Vector[(Element[vecposX, i], Element[vecposY, j]), (Element[vecposX, i] + (vecmag * Element[vecposY, j]), Element[vecposY, j] - (vecmag * Element[vecposX, i]))], i, 1, nv], j, 2, nv)
curvegPart = CurveCartesian(g(t), t, t, -4, y(D))
curvehPart = CurveCartesian(h(t), t, t, -4, y(E))
H: ((0.1 * inth), slidery)
G: ((0.1 * intg), slidery)
F: ((0.1 * intf), slidery)
list2 = Sequence(Text[(10 * i), (i - 0.3, slidery - (6 * sliderdy))], i, -6, 6, sliderdx)