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b Let, f(2)= 2+1 z = 9 D={zec: -4 <Rect? 54,-45 1m (7) 54} Zt1 Im.axis f(Z) 2 B (-3,0) 103) (2+3)(2-3) At Z = 3,-3 f has single pole which lies in the region D. By Cauchy's Residue Real axis (40) A theorem , Stubendz Now, Ze! 20i [Res ( (f;-3) +Res (f, 3)] Res (f;-3) ht (Z+3) f(z) =ht (243). (2x3)(2-3) - Ź 27-3 2+-3 - 3+1 -2 -3-3 -6
Res (f;3) sut (2-3) f(z) 273 ut C Z +1 (2/3).
.
Z-3 (2/3)(2+3) 3+1 4 2 = 3+3 6 3 . Zal 2-9 dz = 2012 ($+ }) - 2101.1 = 20
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