Eval

if t>0 and C is the circle {|z|=3}

Hmm...

Am I suppose to parameterise something?

I can write for example z(t)=3e^{it} then dz = 3i e^{it}dt and sub it back in, but that just makes it messy and complicated.

Am I missing an easier way?

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- June 2nd 2010, 08:10 PMscorpion007cauchy integral formula
Eval

if t>0 and C is the circle {|z|=3}

Hmm...

Am I suppose to parameterise something?

I can write for example z(t)=3e^{it} then dz = 3i e^{it}dt and sub it back in, but that just makes it messy and complicated.

Am I missing an easier way? - June 2nd 2010, 08:23 PMDrexel28
- June 2nd 2010, 08:26 PMscorpion007
Thanks, I considered that just now, but this question belongs to a section well-prior to covering the residue thm, in the CIF section. So I suppose it should be solvable using that...

- June 2nd 2010, 08:36 PMDrexel28
- June 2nd 2010, 09:35 PMscorpion007
I get

but the answer says:

for the partial fractions I got A = B = -1/4 e^{tz}

so we have

where

and

Did I make a mistake? - June 2nd 2010, 09:55 PMDrexel28
- June 2nd 2010, 10:00 PMscorpion007
ah yes! thanks!