Integration in Cylindrical Coordinates

paraboloid z =x2+y2 and the plane z =4. x y z z =x2+y2 It follows that the volume is given by V = ˆ 2π 0 ˆ 2 0 ˆ 4 x2+y2 dzrdrdθ =2π ˆ 2 0 ˆ 4 x2+y2 dzrdr =2π ˆ 2 0 (4−x2−y2)rdr =2π ˆ 2 0 (4−r2)rdr =... =8π Notice also that this solid can be recognized as a solid of revolution. In ................
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