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...Change of variables in double integrals part area the image a region it is often advantageous to evaluate rrr x y da coordinate system other than xy this section we develop method for con verting into iterated systems lets suppose that t u v hf g i map s uv plane onto r and contained rectangle on which both f are di erentiable apartitionofintonsubintervalsofwidth ui andintomsubintervals width covers with collection rectangles if require h j thentheimageoftherectanglesunder regions covering approximately parallelograms aij ijth n m then xx however chapter learned ij where point th thus approxi mately limit as approaches sum leads integral have z areaof dauv dvdu type dudv ii example findanddescribe under transformation hvcos vsin nd solution since vcos cos sin because ranges from an ellipse centered at origin moreover these ellipses completely cover inside corresponding semi major axis minor jacobian determinant uvcos vvsin vvcos uvsin follows du check your reading what variable let be ...