Multiple integrals: Double integrals
Change of variables in double integrals
Using the coordinate transition \(x=u-3v,\;\; y=3u+v\), compute the double integral \[\iint_R x\,y\,\dd(x,y)\] where \(R\) is the rectangle enclosed by the lines \(y=3x\), \(\;y=3x+30\), \(\;3y+x=0\) and \(3y+x=20\). (draw a sketch!)
| \(\iint_R x\,y\,\dd(x,y)={}\) | \(\quad\)where \(R\) is the rectangle enclosed by the given lines. |
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