x

y

%x

ymin = -5.147750349495959
ymax = 5.089013324530572
threshold = 0.03
xmax = 5.14054503589283
xmin = -5.180109784600042
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
A = (3, -3)
B = (2, 4)
curvefFull = Segment(A, B)
f(t) = ((-1) / 7 * (t + 3)) + 3
g(t) = f(t) + (0.4 * ((t - 0.5)^(2) - 3.5^(2))) - (3 * sin(((3 * π) * (t + 3) / 7)))
curvegFull = CurveCartesian(g(t), t, t, -3, 4)
h(t) = f(t) - (0.01 * ((t - 0.5)^(4) - 3.5^(4))) + (0.5 * sin(((11 * π) * (t + 3) / 7)))
curvehFull = CurveCartesian(h(t), t, t, -3, 4)
fintf(t) = (0.5 * (f(t)^(2) + t^(2) - x(A)^(2) - y(A)^(2)))
fintg(t) = (0.5 * (g(t)^(2) + t^(2) - x(A)^(2) - y(A)^(2)))
finth(t) = (0.5 * (h(t)^(2) + t^(2) - x(A)^(2) - y(A)^(2)))
C = Point(curvefFull)
D = Point(curvegFull)
E = Point(curvehFull)
curvegPart = CurveCartesian(g(t), t, t, -3, y(D))
curvehPart = CurveCartesian(h(t), t, t, -3, y(E))
curvefPart = Segment(A, C)
intf: fintf(y(C))
intg: fintg(y(D))
inth: finth(y(E))
inttot: (0.5 * (x(B)^(2) + y(B)^(2) - x(A)^(2) - y(A)^(2)))
all_integrals: "\begin{align*}\dlint &= " + intf + "\\\lint{\adlc}{\dlvf} &=" + intg + "\\ \lint{\sadlc}{\dlvf} &= " + inth + "\end{align*}"
slidery = -4
F: ((0.5 * intf), slidery)
G: ((0.5 * intg), slidery)
H: ((0.5 * inth), slidery)
I: ((0.5 * inttot), slidery)
a: y = slidery
sliderdy = 0.1
vecfield = Sequence(Sequence[Vector[(Element[vecposX, i], Element[vecposY, j]), ((Element[vecposX, i] * (1 + vecmag)), (Element[vecposY, j] * (1 + vecmag)))], i, 1, nv], j, 2, nv)
sliderdx = 1
list1 = Sequence(Segment[(i, slidery - sliderdy), (i, slidery + sliderdy)], i, -6, 6, sliderdx)
list2 = Sequence(Text[(2 * i), (i - 0.1, slidery - (6 * sliderdy))], i, -6, 6, sliderdx)