Let R be the region bounded by the graphs of x+y=1, x+y=2, 2x-3y=2, and 2x-3y+5. Use the change of variables:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

x=1/5(3u+v)[/tex]

[tex]y=1/5(2u-v)[/tex]

to evaluate the integral:

[tex]

\iint(2x-3y)\,dA

[/tex]

I found the jachobian to be -1/5

and the limits of integration to be

1<=u<=2

2<=v<=5

so i set up the integral like this:

[tex]

\frac{-1}{5}\int_{2}^{5}\int_{2}^{1} vdv[/tex]

and I get -21/5 which doesn't seem right(a negitive number??),what am I doing wrong?

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# How to evaluate int 2x-3y dA using change of variables

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