integralr ez dz where gamma is the semicircle from 1 to 1 pa

integral_r e^z dz, where gamma is the semicircle from -1 to 1 passing through i.

Solution

Defined the Y Coordinate points on the Unit Circle (-1,1) equals to (/2, 3/2)

Given _y e^z dz, we know antiderivate of exp is itself so,

_3/2^/2 e^z dz = e^z |

= [e^/2 - e^3/2] + C

this solution can give us a number plus a constant;

= -106.50 + C.