1.2,

Elementary properties\ Let

\\\\gamma :z=z(t),tin(a,b)

. We define the opposite arc, written

-\\\\gamma

, by\

-\\\\gamma :z=z(-t),tin(-b;-a)

\ Then,\

\\\\int_(-7) f(z)dz=\\\\int_(-b)^(-a) f(z(-t))(d)/(dt)[z(-t)]dt=-\\\\int_(-b)^(-a) f(z(-t))(dz)/(dt)(-t)dt=-\\\\int_a^b f(z(t))(dz)/(dt)(t)dt

\ where the last equality is obtained with a simple change of variable. Hence\

\\\\int_(-\\\\gamma ) f(z)dz=-\\\\int_(\\\\gamma ) f(z)dz

1.2 Elementary properties - Let :z=z(t),t(a,b). We define the opposite arc, written , by :z=z(t),t(b,a) Then, 7f(z)dz=baf(z(t))dtd[z(t)]dt=baf(z(t))dtdz(t)dt=abf(z(t))dtdz(t)dt where the last equality is obtained with s simple change of variable. Hence f(z)dz=f(z)dz