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2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel integrals using the contour in the figure. → 0, and show that the contribution from C2 (Hint: To obtain reel integrals in the below take R is O and the contributions of C, and C3 are equal and their sum is equal to total residue lying inside closed contour.) 1 dx x=0 x²+1 а- Im{z} C2 b- Jx=07 dx :- Jr=o x²+1)² Refz} -R R

2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel integrals using the contour in the figure. → 0, and show that the contribution from C2 (Hint: To obtain reel integrals in the below take R is O and the contributions of C, and C3 are equal and their sum is equal to total residue lying inside closed contour.) 1 dx x=0 x²+1 а- Im{z} C2 b- Jx=07 dx :- Jr=o x²+1)² Refz} -R R

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Assume that x,y E R and z = x+iy E C and answer the followings.

2- Assume that x, y ER and z = x + iy E C and answer the followings. Calculate the reel integrals using the contour in the figure. (Hint: To obtain reel integrals in the below take R → o, and show that the contribution from C2 is O and the contributions of C, and C3 are equal and their sum is equal to total residue lying inside closed contour.) а- dx Im{z} b- Jx=0 x* +1 1 C- (x²+1)2 Refz) -R R
Transcribed Image Text:2- Assume that x, y ER and z = x + iy E C and answer the followings. Calculate the reel integrals using the contour in the figure. (Hint: To obtain reel integrals in the below take R → o, and show that the contribution from C2 is O and the contributions of C, and C3 are equal and their sum is equal to total residue lying inside closed contour.) а- dx Im{z} b- Jx=0 x* +1 1 C- (x²+1)2 Refz) -R R
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