Multiple integrals: Double integrals
Change of variables in double integrals
Using the coordinate transition \(x=u-v,\;\; y=u+v\), compute the double integral \[\iint_R x\,y\,\dd(x,y)\] where \(R\) is the rectangle enclosed by the lines \(y=x\), \(\;y=x+4\), \(\;y+x=0\) and \(y+x=6\). (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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