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**Unformatted text preview: **) rdrd Lecture 13: Polar Coordinates Class exercise Find the volume of the solid bounded by the paraboloid z = 1 + 2 x 2 + 2 y 2 and the plane z = 7. Lecture 13: Polar Coordinates Class exercise Find the volume of the solid bounded by the paraboloid z = 1 + 2 x 2 + 2 y 2 and the plane z = 7. Answer: 9 4 Lecture 13: Polar Coordinates Using polar coordinates for general regions. Dene a region as D = { ( r , ) | , h 1 ( ) r h 2 ( ) } , then ZZ D f ( x , y ) dA = Z Z h 2 ( ) h 1 ( ) f ( r cos , r sin ) rdrd Lecture 13: Polar Coordinates Class exercise Z a Z- a 2-y 2 x 2 ydxdy Lecture 13: Polar Coordinates Class exercise Z a Z- a 2-y 2 x 2 ydxdy Answer: a 5 15 Lecture 13: Polar Coordinates...

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