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Thread: change of variables (bounds)

  1. #1
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    change of variables (bounds)

    Hey guys,

    I am really confused while changing the bounds when we do the change of variables.

    Given, u=x and v= 2y-x. Integrating f(x,y) dy dx. where (x/2) < y<(x/2)+1 , and 0<x<2. How do I change the bounds in terms of du dv.

    Thanks guys.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Your region is a paralellogram whose coordinates are $\displaystyle (0,0),(2,1),(2,2),(0,1).$ With the given change of variables put those $\displaystyle (x,y)$ into $\displaystyle (u,v)=(x,2y-x).$ to get the new region for $\displaystyle (u,v).$
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