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Multivariable CalculusMediumChange of Variables & the Jacobian

Change of Variables & the Jacobian · Medium problem

A heating element's output is modeled by f(x,y)=x2+y2f(x,y)=x^2+y^2 over a half-disk tray of radius 33 (where y≥0y\ge0). Using polar coordinates, find ∬D(x2+y2) dA\displaystyle\iint_D (x^2+y^2)\,dA over the tray.