# VC4.9

From Example Problems

Let C1 denote the curve made up of the straight lines AB,BC and CA. Since the integration is performed in the xy-plane,we have . Then the required integral around the triangle ABC is given by

=

=

Here on AB,y=0,dy=0 and x varies from 0 to 2. On BC,x=2,dx=0 and y varies from 0 to 1. Now,equation of the line CA is

Therefore,on CA, and y varies from 1 to 0. Using the above,

=

=