Lesson_11 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 11...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 11 lebxz daiib ixei :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd mieqn lxbhpi` mieqnd lxbhpi`d ly zepekz :miiwzn α, β mireawe [ a, b ] rhwa f, g zeiliaxbhpi` zeivwpet izy lkl . b Z a ( αf ( x ) + βg ( x ) ) d x = α b Z a f ( x )d x + β b Z a g ( x )d x (1) . b Z a f ( x )d x = c Z a f ( x )d x + b Z c f ( x )d x if` a < c < b m` (2) . b Z a f ( x )d x ≤ b Z a g ( x )d x if` x ∈ [ a, b ] lkl f ( x ) ≤ g ( x ) m` (3) b Z a f ( x )d x ≤ b Z a f ( x ) d x :miiwzne ,ziliaxbhpi` | f | divwpetd mb (4) :dxrd . a, b, c zecewp ly dxiga lkl miiwzn (2) df oeniq mr . a Z b f ( x )d x =- b Z a f ( x )d x oenqa ynyp 1 htyn .ziliaxbhpi` `id zetivx-i` zecewp ly iteq xtqn wx dl yiy dneqg divwpet zxfra `l` dxcbdd it-lr zexiyi lxbhpi`d z` miaygn oi` k"xca uipaiil - oeheip zgqep if` .dly dnecw divwpet F ( x ) idze [ a, b ] rhwa dtivx divwpet f ( x ) idz b Z a f ( x )d x = F ( b )- F ( a ) 1 . 1 Z x 2 d x z` aygp :`nbec :oexzt 1 Z x 2 d x = x 3 3 1 = 1 3 lawzn , f ( x ) = x 2 ly dnecw divwpet `id F ( x ) = x 3 3-y xg`n mighy iaeyig 1 libxz . [1 , 2] rhwa mi- x-d xiv oial f ( x ) = ln x divwpetd ly sxbd oia labend ghyd z` eayg :oexzt : f ( x ) = ln x divwpetd sxb z` hhxyp :i"r oezp ghyd okl 2 Z 1 ln x d x = ( * ) ( x ln x- x ) 2 1 = (2 ln 2- 2)- (1 ln 1- 1) = 2 ln 2- 1 mr miwlga divxbhpi`a dyrp ln x ly miieqn `ld lxbhpi`d aeyig- ( * ) u ( x ) = ln x v ( x ) = 1 u ( x ) = 1 x v ( x ) = x zeivwpet xtqn ly mitxb i"r meqgd ghyd , g ( x ) divwpetd ly sxbd i"r dhnlne f ( x ) divwpetd ly sxbd i"r dlrnln meqg D megz m` :i"r ozip D megzd ly ghyd f` , [ a, b ] rhwa `vnp x xy`k S ( D ) = b Z a ( f ( x )- g ( x ) ) d x 2 2 libxz mdly ybtnd zcewpn y = e- x- e y = e x ly mitxbd i"r meqgd megzd ly ghyd z` eayg . x = 1...
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Lesson_11 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 11...

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