Let IR represent the contour consisting of the upper half of the circle |z| = R...

 

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Let IR represent the contour consisting of the upper half of the circle |z| = R for R > 2 taken in the counterclockwise direction (note that the contour is just the semicircle; it is not a closed contour). Show that 222-1 24 +52 +4 TR(2R + 1) dz (R - 1) (R - 4) R Conclude that the value of the integral tends to 0 as R . Let IR represent the contour consisting of the upper half of the circle |z| = R for R > 2 taken in the counterclockwise direction (note that the contour is just the semicircle; it is not a closed contour). Show that 222-1 24 +52 +4 TR(2R + 1) dz (R - 1) (R - 4) R Conclude that the value of the integral tends to 0 as R .