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Integral Calculus

evaluate cyclic integration of[ 3*(z)square +7z+1]dz\z+1,where c is a circle and b=mode of z+i=1,solve by using residue

animesh CHOUBEY

15 Years agoGrade

1 Answer

Jitender Singh

12 Years ago

Ans:

$I = \oint \frac{3z^{2}+7z+1}{z+1}dz$

$I = \oint \frac{3z^{2}+7z+1}{(z-(-1)^{1}}dz$

$I = 2\pi i Residue (z=-1)f(z)$

$Residue (z=-1)f(z) = 3z^{2}+7z+1|_{z = -1}$

$Residue (z=-1)f(z) = 3(-1)^{2}+7(-1)+1 = -3$

$I = -6\pi i$

Thanks & Regards

Jitender Singh

IIT Delhi

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