Lesson_12 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 12...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 12 lebxz xlw ilp :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd (miizin` `l) millken milxbhpi` 1 (-∞ , b ] , [ a, + ∞ ) enk miiteqpi` mirhw lr mb legi `edy dfk ote`a lxbhpi`d byen z` aigxp-hpi` .zeneqg gxkda opi`y zeivwpet lr mb legi `ed jkl sqepa . (-∞ , + ∞ ) elek xyid lr mbe .millken milxbhpi` mi`xwp df beqn milxb oey`x beqn llken lxbhpi` 1.1 1 dxcbd (iteqe) miiw `ad leabdy jk [ a, + ∞ )-l iwlgy xebq rhw lka ziliaxbhpi` divwpet f ( x ) idz . lim b → + ∞ b Z a f ( x )d x = I f ( x ) ly llkend lxbhpi`d ik mb xn`pe , [ a, + ∞ ) rhwa f ( x ) ly llkend lxbhpi`d `xwp I f` .xcazn lxbhpi`dy xn`p ,iteq `l e` miiw `l leabd m` .qpkzn [ a, + ∞ ) rhwa :meyxl lkep + ∞ Z a f ( x )d x = lim b → + ∞ b Z a f ( x )d x : (-∞ , a ] oxwa llkend lxbhpi`d z` mixicbn dnec ote`a a Z-∞ f ( x )d x = lim b →-∞ a Z b f ( x )d x . (-∞ , + ∞ ) xyid lka izin` `l lxbhpi` mb xicbdl lkep ,xebq rhw lka ziliaxbhpi` f ( x ) m` :xicbpe a idylk dcewp xgap + ∞ Z-∞ f ( x )d x = a Z-∞ f ( x )d x + + ∞ Z a f ( x )d x m` .qpkzn il`nyd sb`ay lxbhpi`d ik xn`p f` ,miqpkzn ipnid sb`a milxbhpi`d ipy m` .xcazn lxbhpi`dy xn`p f` xcazn miipyd oian cg` elit` 1 1 libxz .dxcbdd i"tr + ∞ Z d x 1 + x 2 lxbhpi`d ly zeqpkzd wecap :oexzt + ∞ Z d x 1 + x 2 = lim b → + ∞ b Z d x 1 + x 2 = lim b → + ∞ arctan x b = lim b → + ∞ (arctan b- arctan 0) = π 2- 0 = π 2 . π 2 ekxre qpkzn lxbhpi`d okl ,iteqe miiw leabd 2 libxz .dxcbdd i"tr + ∞ Z-∞ d x 1 + x 2 lxbhpi`d ly zeqpkzd wecap :oexzt + ∞ Z-∞ d x 1 + x 2 = Z-∞ d x 1 + x 2 + + ∞ Z d x 1 + x 2 = lim a →-∞ Z a d x 1 + x 2 + lim b → + ∞ b Z d x 1 + x 2 = lim a →-∞ arctan x a + lim b → + ∞ arctan x b = lim a →-∞ (arctan 0- arctan a ) + lim b → + ∞ (arctan b- arctan 0) =- - π 2 + π 2- 0 = π . π-l qpkzn oezpd lxbhpi`d okl ,miqpkzn oini cva milxbhpi`d ipy :zexrd-hpi`d ly zeqpkzdd jnq lr mb Z-∞ d x 1 + x 2 lxbhpi`d zeqpkzd lr dpwqnl ribdl xyt` • . 1 1 + x 2 divwpetd zeibefe + ∞ Z d x 1 + x 2 lxb lxbhpi`d a, b lkly iptn ,lxbhpi`d z` lvtl mixgea dcewp dfi`a aeyg `ly mb xikfp • ....
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Lesson_12 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 12...

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