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...Double integrals in polar coordinates part the area di erential wecanalso apply change of variable formula to coordinate trans formation x rcos y rsin however due importance we derive its more rigorously begin with jacobian determinant is cos sin r as a result for da drd rdrd let us consider now region s dened by g f where and are contained all if m an h ne partition rn then image near parallelograms whose areas denoted ajk since parallelogram approximately jk j so that k n lim xx limxx writing each these limits results zz z aid use notice p constant circle radius centered at origin xy plane while ray angle beginning moreover corresponds example toevaluate px dydx solution do transform iterated integral into sector ris between thus becomes resulting easily evaluated d check your reading what does correspond volumes bounded implies areaof allowing nd findthearea or sec line from evaluation leads tan can regions enclosed graphs functions whatistheareaoftheregion car dioid sincethecardioi...