Integral with cauchy formula

  • #1
114
0

Homework Statement


using cauchy integral formula calculate
[tex]\int\limits_C\frac{e^{2z}}{z^2-4}\mbox{d}z[/tex]
where [tex]C[/tex] is closed curve (point [tex]z=2[/tex] is inside)

The Attempt at a Solution


[tex]\ldots=\int\limits_C\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z=\int\limits_C\frac{f(z)}{z-2}\mbox{d}z=2\pi if(2)=2\pi i\frac{e^{2\cdot2}}{4}=\frac12\pi e^4i[/tex]
is it correct?
 

Answers and Replies

  • #2
1,101
3
Yes, and yes for the other one where C is an ellipse.
 

Related Threads on Integral with cauchy formula

  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
958
  • Last Post
Replies
2
Views
12K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
832
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
8
Views
2K
Top