• Support PF! Buy your school textbooks, materials and every day products Here!

Calculate complex integral as line integral

  • Thread starter evol_w10lv
  • Start date
  • #1
71
0

Homework Statement


We need to calculate this complex integral as line integral:
mvw98gi92v0r12s9uk9w.png



Homework Equations





The Attempt at a Solution


This is correct, I guess:
v8yzkdwcftef6j9gch6p.png


But not sure about this part:
o09jbdaoynkhyxn1jg0x.png


Are dx, dy, x, y chages correct or there is other method to use?
 

Answers and Replies

  • #2
1,796
53

Homework Statement


We need to calculate this complex integral as line integral:
mvw98gi92v0r12s9uk9w.png



Homework Equations





The Attempt at a Solution


This is correct, I guess:
v8yzkdwcftef6j9gch6p.png


But not sure about this part:
o09jbdaoynkhyxn1jg0x.png


Are dx, dy, x, y chages correct or there is other method to use?
Not hard to numerically integrate it and check your results right?

Code:
NIntegrate[(z^2 + z*Conjugate[z])*I*Exp[I*t] /. z -> Exp[I*t], {t, Pi, 0}]
but I just let [itex]z=e^{it}[/itex] to check that. What's wrong with just doing that symbolically from the start.
So my suggestion is for you to compute the expression your derived, compute it numerically in Mathematica or other, and thirdly, by letting [itex]z=e^{it}[/itex] and computing it by evaluating the integral in t and then compare the three.
 
  • #3
71
0
Of course... thanks for idea. I cheked results and they were equal.
 
Top