HdHWLineIntegral.nb
Lines := ListLinePlot @8880, 0<, 8Exp@0 - 1D, 0 ´ 0<<,
881  2, 1  H2 Sqrt@2DL<, 81  2 + Exp@1  2 - 1D, 1  H2 Sqrt@2DL + 1  2 * 1  H2 Sqrt@2DL<<,
881, 1<, 81 + Exp@1 - 1D, 1 + 1 ´ 1<<<, PlotStyle ® ThickD
Curve := ParametricPlot @8t ^ 2, t ^ 3<, 8t, 0, 1<D
Show@Lines, CurveD
2.0
1.5
1.0
0.5
0.5
1.0
1.5
2.0
Field := VectorPlot@8Exp@x - 1D, x y<, 8x, 0, 1<, 8y, 0, 1<D
Show@Field, CurveD
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Arrows := ListVectorPlot @
8880, 0<, 8Exp@0 - 1D, 0 ´ 0<<, 881  2, 1  H2 Sqrt@2DL<, 8Exp@1  2 - 1D, 1  2 * 1  H2 Sqrt@2DL<<,
881, 1<, 8Exp@1 - 1D, 1 ´ 1<<<, VectorPoints ® AllD
1
HdHWLineIntegral.nb
Show@Arrows, CurveD
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
In[7]:=
ForceField := VectorPlot@8x ^ 2, x y<, 8x, - 2, 2<, 8y, - 2, 2<D
In[5]:=
CirclePath := ParametricPlot @82 Cos@tD, 2 Sin@ tD<, 8t, 0, 2 Pi<D
In[8]:=
Show@ForceField, CirclePathD
2
1
Out[8]=
0
-1
-2
-2
-1
0
1
2
2