Fix >0.

Evaluate the integral

0t2t4+a4dt

by integrating

f(z)=1z2+2

in the counterclockwise direction around the boundary of the region

{zC|0|z|R,0Argz4}

and then letting R.

Fix a >0. Evaluate the integral +2 dt 0 14+ 04 by integrating f ( z) = 2 2 + 02 in the counterclockwise direction around the boundary of the region { z E C|0