"Green's theorem"

clear
P = 2x^3 - y^3
Q = x^3 + y^3
f = d(Q,x) - d(P,y)
x = r cos(theta)
y = r sin(theta)
T = defint(f r,r,0,1,theta,0,2pi)
check(T = 3/2 pi)

clear
x = cos(t)
y = sin(t)
P = 2x^3 - y^3
Q = x^3 + y^3
f = P d(x,t) + Q d(y,t)
f = circexp(f)
T = defint(f,t,0,2pi)
check(T = 3/2 pi)

clear
P = 1 - y
Q = x
x = 2 cos(t)
y = 2 sin(t)
T = defint(P d(x,t) + Q d(y,t),t,0,2pi)
check(T = 8 pi)

x = quote(x) --clear x
y = quote(y) --clear y
h = sqrt(4 - x^2)
T = defint(d(Q,x) - d(P,y),y,-h,h,x,-2,2)
check(T = 8 pi)

f = d(Q,x) - d(P,y) -- do before change of coordinates
x = r cos(theta)
y = r sin(theta)
T = defint(f r,r,0,2,theta,0,2pi)
check(T = 8 pi)

T = defint(f r,theta,0,2pi,r,0,2) -- try integrating over theta first
check(T = 8 pi)
