X - To dx 1 + x For each of the two integrals: A := dx...

 

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X - To dx 1 + x¹² For each of the two integrals: A := dx a. Draw an annotated diagram for each integral; indicate the location and nature (pole?, branch-point?, order?) of each singularity of the integrand. with a > 0, and B := b. Close the integration contour by adding contour segments along which the integral is either otherwise known or proportional to A, i.e., B, respectively. Sketch your contour clearly. c. If there are poles along the contour, determine the detour. d. Evaluate the closed contour integral by summing the enclosed residues. e. Finally, compute the value of the above real integrals A and B. X - To dx 1 + x¹² For each of the two integrals: A := dx a. Draw an annotated diagram for each integral; indicate the location and nature (pole?, branch-point?, order?) of each singularity of the integrand. with a > 0, and B := b. Close the integration contour by adding contour segments along which the integral is either otherwise known or proportional to A, i.e., B, respectively. Sketch your contour clearly. c. If there are poles along the contour, determine the detour. d. Evaluate the closed contour integral by summing the enclosed residues. e. Finally, compute the value of the above real integrals A and B.

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ANSWER a The first integral A is A xx2x2 dx The integrand can be written as xx2x2 xx1 1 The denomina... View the full answer