Unformatted text preview: S in the Form oF a graph z1 = g ( x, y ) =Â² 4x 2y 2 where ( x, y ) âˆˆ D = { ( x, y ); 3 â‰¤ x 2 + y 2 â‰¤ 4 } . dS = dxdy/  n Â· k  = Âµ 1 + g 2 x + g 2 y dxdy = ... = 2 dxdy/ Â² 4x 2y 2 so Area( S ) = Â±Â± S dS = Â±Â± D dxdy Â² 4x 2y 2 = Â± 2 âˆš 3 Â± 2 Ï€ rdrdÎ¸ âˆš 4r 2 =2 Ï€ Â² 4r 2 Â¶ Â¶ Â¶ Â¶ 2 âˆš 3 = 2 Ï€ Â±Â±Â± B x 2 dxdydz = Â± 2 Â± 2 Ï€ Â± Ï€ r 2 sin 2 Ï† cos 2 Î¸ r 2 sin Ï† dÏ†dÎ¸dr = Â± 2 Â± 2 Ï€cos 3 Ï† 3 Â¶ Â¶ Â¶ Â¶ Ï€ cos 2 Î¸ r 4 dÎ¸dr = 2 3 r 5 5 Â¶ Â¶ Â¶ Â¶ 2 Â± 2 Ï€ cos 2 Î¸dÎ¸ = 2 3 2 5 5 Ï€ NOTE: THERE ARE NO SOLUTIONS TO PROBLEMS 69!...
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 Spring '09
 STAFF
 Math, Trigraph, Graph of a function, 2 j, dx dy

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