Change of limits

1. Jan 18, 2009

terryfields

rite ive got limits of 0<x<pi/2 and x-pi<y<x

with u=x-y, v=x+y

with a transformation from f(x,y) to f(u,v) which isnt really needed for what im about to ask

i get he jacobian as 1/2
then get y=(v-u)/2 and x=(u+v)/2 all of which i know is right as i have the answers, this is purely revision
then when changing the limits i get every step until the last one which are
0<x<pi/2
0<(u+v)/2<pi/2
0<u+v<pi
-u<v<pi-u
0<u<pi<<<<<<<<<<<where does that come from

2. Jan 18, 2009

terryfields

similarly x-pi<y<x
(u+v)/2-pi<v-u<(u+v)/2
-2pi<-2u<0
-u<v<pi-u