Example: Evaluate zdx dy dz ken over the regíon common to the surfaces x+y+ z = a, and x + y2 = ax A Solution. The region is bounded, above and below by the sur

Example: Evaluate zdx dy dz ken over the regíon common to the surfaces x+y+ z = a, and x + y2 = ax A Solution. The region is bounded, above and below by the surfaces Z= ya-x - y and z=-ya - x - y zdx dy dz = | dx dy|_-7 a-x-yyh dx dy s projection on the xy-plane is the circular domain D = +y < ax rva-x-y) dz Changing ST, 0srsa cos ) O polars, the region D becomes the circle, r a cos hoa e chwemit o e not egoal uhy yng e o ra cos 0 (a-r23r dr 15 (1-sin' 0)de = 2a(15T-16) 225 nlact Us Mnit 1800-120-1021 474