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Let $I_r= \int dz/(z(z-1)(z-2))$ along $C_r$, where $C_r = \{z\in\mathbb C : |z|=r\}$, $r>0$. Then

a. $I_r= 2\pi i$ if $r\in (2,3)$

b. $I_r= 1/2$ if $r\in (0,1)$

c. $I_r= -2\pi i$ if $r\in (1,2)$

d. $I_r= 0$ if $r>3$.

I am stuck on this problem . Can anyone help me please?

all options are looking wrong by using residue theorem......

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    For rє(2,3), if I take r=2.5 etc……………. All the options are wrong???2012-12-17
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    For rє(2,3), if I take r=2.5 etc............ and i used residue theorem but none of the options is correct in my calculaton.......am i right????2012-12-17
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    For rє(2,3),can I take r=2.5 etc. or not?????????2012-12-17
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    For rє(2,3), if I take r=2.5 etc……… using residue theorem Ir = 2Πi(sum of residue)=2Πi(2-1+2)=6Πi so option a is wrong am i right??????????2012-12-17

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