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

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