infi2HW13 - # 1 2 dxdy .2 :zeleaxtd i"r meqgd megzd...

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13 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2008 lixt`l 17 :dybd jix`z A 4 lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz sca jxev oi` .oeilib xtqne ,f"z ,zeny xexiaa oiivl `p .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry 1 libxz | f ( x,y ) | ≤ μ ( y ) miiwzn x [ a,b ] lkly jk dtivx μ ( y ) zniiw ik oezp . R 2 - a dtivx f ( x,y ) idz :qpkzn `ad llkend lxbhpi`d oke Z c μ ( y ) dy :egiked . [ a,b ] - a dtivx g ( x ) = R c f ( x,y ) dy divwpetd .1 :miiw `ad llkend letkd lxbhpi`d .2 ZZ [ a,b ] × [ c, ) f ( x,y ) dxdy :oeieeiyd miiwzn .3 Z b a ±Z c f ( x,y ) dy dx = ZZ [ a,b ] × [ c, ) f ( x,y ) dxdy = Z c ±Z b a f ( x,y ) dx dy 2 libxz :mi`ad milxbhpi`d z` eayg i"r meqgd megzd `ed D xy`k , ZZ D ( x + y ) 3 ( x - y ) 3 dxdy .1 . x + y = 1; x + y = 3; x - y = 1; x - y = - 1; D = { ( x,y ) | x 2 a 2 + y 2 b 2 1 } xy`k , ZZ D " 1 - ± x 2 a 2 + y 2 b 2 1 2
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Unformatted text preview: # 1 2 dxdy .2 :zeleaxtd i"r meqgd megzd `ed D xy`k , ZZ D x 2 sin( xy ) y dxdy .3 . y 2 = π 2 x ; y 2 = πx ; x 2 = y ; x 2 = 2 y ; xy`k , ZZ D y (4 x-sin2 x ) 2 x sin 2 x tan x dxdy .4 . D = { ( x,y ) | 2tan x ≤ y ≤ 4tan x, y 2 ≤ x ≤ 2 y 2 } 1 ewca !llken lxbhpi` df) . D = { ( x,y ) | x ≥ 1 , ≤ y ≤ π 4 } megza ZZ D sin y xe x cos y dxdy .5 .(mipyip milxbhpi` i"r eaeyigl mi`pzd miniiwzny 3 libxz :( < c < d- e < a < b ) dveawd ghy z` eayg A = { ( x,y ) ∈ R 2 | x > , y > , ay ≤ x 3 ≤ by, cx ≤ y 3 ≤ dx } 2...
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This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Winter '08 term at Technion.

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infi2HW13 - # 1 2 dxdy .2 :zeleaxtd i"r meqgd megzd...

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