Question 2 1 Consider the contour integral P. T-2 + 4)²' dz where C is the closed contour consisting of the real axis from –R to +R and the semicircle I centered at the origin, of radius R,in the...

Extracted text: Question 2 1 Consider the contour integral P. T-2 + 4)²' dz where C is the closed contour consisting of the real axis from –R to +R and the semicircle I centered at the origin, of radius R,in the upper half z-plane. 1 (a) Find the poles of the integrand their orders and the residues at the poles (2² + 4)2’ (b) Letting R → x, use the Residue theorem to evaluate the real integral 1 dx (x² + 4)2