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GATE EC 2021 Set 1 — Question 36

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MCQ+2 / -0.67MediumResidue Theorem & Contour IntegrationComplex AnalysisEngineering Mathematics

Engineering Mathematics → Complex Analysis → Residue Theorem & Contour Integration

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Question

Consider the integral∮Csin⁡(x)x2(x2+4)dx\oint_C \frac{\sin(x)}{x^2(x^2 + 4)} dxwhere CC is a counter-clockwise oriented circle defined as ∣x−i∣=2|x - i| = 2. The value of the integral is
  1. A.
    −π8sin⁡(2i)-\frac{\pi}{8} \sin(2i)
  2. B.
    π8sin⁡(2i)\frac{\pi}{8} \sin(2i)
  3. C.
    −π4sin⁡(2i)-\frac{\pi}{4} \sin(2i)
  4. D.
    π4sin⁡(2i)\frac{\pi}{4} \sin(2i)

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