Complex Integration

kmeado07

1. The problem statement, all variables and given/known data

Evaluate the following intergral:


2. Relevant equations

Intergral from gamma of (y)dz, where gamma is the union of the line segments joining 0 to i and then i to i+2

3. The attempt at a solution

I have no idea how to do this!

tiny-tim

Hi kmeado07!

(have a gamma: Γ )

Γ is an L-shaped path …

just integrate along each bit of it separately.

(but what is y? )

HallsofIvy

Presumably, if you are expected to do a problem like this, you know something about path integrals. The line from 0 to i, in the complex plane, can be written as z= (1+i)t where t ranges from 0 to 1. The line from i to i+ 2 can be written as z= (1+ t)+ i where, again, t ranges from 0 to 1. Do those two integrals separately with z replace by those and dz by (1+i)dt in the first integral and by dt in the second.

Unfortunately, you see to have forgotten to say what the integrand, y(z), is!