Multiple integrals: Double integrals
Change of variables in double integrals
Using the coordinate transition \(x=u-2v,\;\; y=2u+v\), compute the double integral \[\iint_R x\,y\,\dd(x,y)\] where \(R\) is the rectangle enclosed by the lines \(y=2x\), \(\;y=2x+15\), \(\;2y+x=0\) and \(2y+x=15\). (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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