Question 2

In this activity, you will work through a proof of a special case of Green's The- orem. In this special case, we onlj},r consider regions R enclosed by a simple closed smooth curve C oriented in the counterclockwise direction, such that the region can be expressed in two ways I R: {[r,y}: a 5 1.- E b,'1[.r} 5 y 3 132(3)} or I R: Hay}: Hllyl EIEHaiyl: 5355} Under these conditions, we prove the circulation form of Green's Theorem: 11====111-)= We begin by splitting up the double integral and analyzing each piece. 11121-1)\" =113:= 111M of 1. Show that dy dA = (f(z, Gz(x)) - f(x, G,(x) dr 2. Notice that, over the interval a