(* FILE: lineint090311.m; [06p58] *)
(* USAGE: << lineint090311.m *)
(* Output:
In[1]:= <<lineint090311.m
     8 I
10 - ---
      3

10 - 8 I

33
--
2

44  5  103
--  -  ---
3   2   6

97
--
6        *)

ClearAll[t,z,f,ans]
(* a *)
f[z_]:=Re[z]-I*Im[z];
t=Re[T];
z=t^2+t*I;
ans=Integrate[f[z]*D[z,t],{t,0,2}];
Print[ans];
Clear[t,z]

(* b *)
ans=Integrate[f[z],{z,0,2*I}]+Integrate[f[z],{z,2*I,2*I+4}];
Print[ans];
Clear[f];

(* c *)
f[x_,y_]:={2*y+x^2,3*x-y};
x=2*t;
y=t^2+3;
{xx,yy}=Integrate[f[x,y]*D[{x,y},t],{t,0,1}];
Print[xx+yy];
Clear[x,y,xx,yy];

(* d *)
x=2*t;
y=3;
{xx,yy}=Integrate[f[x,y]*D[{x,y},t],{t,0,1}];
b1=xx+yy;
Clear[x,y,xx,yy];

x=2;
y=t^2+3;
{xx,yy}=Integrate[f[x,y]*D[{x,y},t],{t,0,1}];
b2=xx+yy;
Print[b1, "  ", b2, "  ", Simplify[b1+b2]]
Clear[x,y,xx,yy,b1,b2];

(* e *)
x=2*t;
y=t+3;
{xx,yy}=Integrate[f[x,y]*D[{x,y},t],{t,0,1}];
Print[xx+yy];
Clear[x,y,xx,yy];



