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The value of the integral

evaluated using contour integration and the residue theorem is
  • a)
    -π sin (1)/e
  • b)
    -π cos (1)/e
  • c)
    sin (1)/e
  • d)
    cos (1)/e
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The value of the integralevaluated using contour integration and the r...

Concept:
Cauchy Integral Theorem:

 
Where z = a be any point inside the close region.
Cauchy’s Residue Theorem:
= Sum of Residue at Pole or singularity with in the region
Res at z = a

Calculation:
We know that eix = cos x + i sin⁡ x
Let x replace by z.

Now, z2 + 2z + 2 = 0 then roots of z are:


 
z = -1 ± i is the only pole lying in f(z) > 0
Here n = 1

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The value of the integralevaluated using contour integration and the residue theorem isa)-π sin (1)/eb)-π cos (1)/ec)sin (1)/ed)cos (1)/eCorrect answer is option 'A'. Can you explain this answer?
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