Thread: Line Integrals

Evaluate the line integral where C consists of the top half of the circle from (1,0) to (-1,0) and the line segment from (-1,0) to (-2,3)

I got 0 for the line integral over the circle, and over the line segment. However, the answer provided is . Can someone check?

Also, anyone know a way to evaluate line integrals on Mathematica?

Your line integral is right, I just checked. Maybe the arc needs to be expressed solely in terms of x or y, rather than ? For example replace y with . However the integral becomes very complicated after that..

Thanks, I'll ask my TA if she possibly made a mistake.

Originally Posted by Andrew007

Your line integral is right, I just checked. Maybe the arc needs to be expressed solely in terms of x or y, rather than ? For example replace y with . However the integral becomes very complicated after that..

Quick question though: would such a substitution change anything? It's still the same expression.

Originally Posted by MathTooHard

Also, anyone know a way to evaluate line integrals on Mathematica?

Mathematica can do line integrals if you supply the parameterization:

Here's yours:

Code:

In[24]:=
x[t_] := Cos[t]; 
y[t_] := Sin[t]; 
Integrate[Sin[x[t]]*Derivative[1][x][t], 
   {t, 0, Pi}] + Integrate[
   Cos[y[t]]*Derivative[1][y][t], 
   {t, 0, Pi}]
x[t_] := t; 
y[t_] := -3*t - 3; 
Integrate[Sin[x[t]]*Derivative[1][x][t], 
   {t, -1, -2}] + Integrate[
   Cos[y[t]]*Derivative[1][y][t], 
   {t, -1, -2}]

Out[26]=
0

Out[29]=
Cos[1] - Cos[2] + Sin[3]