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Change of limits

  1. Jan 18, 2009 #1
    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. jcsd
  3. Jan 18, 2009 #2
    similarly x-pi<y<x
    (u+v)/2-pi<v-u<(u+v)/2
    -2pi<-2u<0
    -u<v<pi-u
     
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