{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson_11

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}