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         <title><![CDATA[INTEGRALE DEFINITE]]></title>
        <description><![CDATA[Definiţii şi teoreme, interpretări geometrice, proprietăţi şi aplicaţii practice (arii&nbsp;de suprafeţe plane şi de rotaţie, lungimi de arce de curbă, volume şi centre de greutate) sunt prezentate, succint, &icirc;n prezentul capitol.&nbsp;&nbsp;]]></description>
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					<title><![CDATA[DEFINITII]]></title>
					<description><![CDATA[Suma Riemann (sau suma integrala) asociata functiei f, diviziunii &Delta; şi sistemului de puncte intermediare&nbsp;xi ,&nbsp;este numărul real:$latex {##sigma}_{##Delta}{(f,##xi)}=##sum_{i=1}^{i=n}{f{({##xi}_i)}}##cdot{({{x}_{i}}-{{x}_{i-1}}}).$ Definitie: Functia f, definita pe intervalul [a,...]]></description>
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					<pubDate>Sun, 07 Dec 2008 01:46:52 +0200</pubDate>
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					<title><![CDATA[PROPRIETATI]]></title>
					<description><![CDATA[Formula&nbsp;Leibniz-Newton: Fie f o functie definita pe un interval [a,b] si cu valori in R, integrabila, care admite primitive pe [a,b]. Atunci, pentru orice primitiva F a functiei f, are loc egalitatea:$latex ##int_{a}^{b}{f(x){dx}}=F(b)-F(a).$ Teorema lui&nbsp;Lebesgue (cazul finit): Fie&nbsp...]]></description>
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					<pubDate>Sun, 12 Jun 2011 21:15:00 +0300</pubDate>
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					<title><![CDATA[METODE DE CALCUL]]></title>
					<description><![CDATA[Metoda integrarii prin parti:Fie functiile f si g, definite pe intervalul [a, b] si cu valori in R,&nbsp;derivabile, cu derivatele continue.&nbsp;Atunci:$latex ##int_{a}^{b}{f(x)}##cdot{g'(x)}{dx}={f(x)}##cdot{g(x)}{|}_{a}^{b}-##int_{a}^{b}{f'(x)}##cdot{g(x)}{dx}$ (formula integrarii prin parti)....]]></description>
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					<pubDate>Sun, 03 Apr 2011 00:13:00 +0300</pubDate>
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					<title><![CDATA[EXEMPLUL 1]]></title>
					<description><![CDATA[Suport teoretic:Integrale definite, metoda intai a schimbarii de variabila, metoda integrarii prin parti.Enunt:Sa se calculeze integrala definita:$latex I=##int_1^{e^{##frac{##pi}{2}}}{{sin}(lnx)}{dx}.$&nbsp;Raspuns:$latex I=##frac{##sqrt{e^{##pi}+1}+1}{2}.$]]></description>
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					<pubDate>Thu, 15 Jul 2010 10:49:00 +0300</pubDate>
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					<title><![CDATA[EXEMPLUL 2]]></title>
					<description><![CDATA[Suport teoretic:Integrala definita, prima metoda a schimbarii de variabila, formula Leibniz-Newton, formule de derivare si primitivare, proprietati ale logaritmilor.Enunt:Sa se calculeze integrala definita:$latex I=##int_{1}^{2}{##frac{x##sqrt{ln(x^2+1)}}{x^2+1}}{dx}.$Raspuns:$latex I={ln}{##sqrt...]]></description>
					<link>http://www.profesoronline.ro/exemplul_2.html?axBA2064xABdxBA2609xABbxBAartDet</link>
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					<pubDate>Tue, 26 Oct 2010 11:51:00 +0300</pubDate>
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					<title><![CDATA[EXEMPLUL 3]]></title>
					<description><![CDATA[Suport teoretic:Integrala definita, functie impara.Enunt:Sa se calculeze urmatoarea integrala definita:$latex I=##int_{-##frac{##pi}{2}}^{##frac{##pi}{2}}{##frac{xcosx}{1+x^2}}{dx}.$Raspuns:I = 0.]]></description>
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					<pubDate>Thu, 16 Jun 2011 10:42:00 +0300</pubDate>
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					<title><![CDATA[EXEMPLUL 4]]></title>
					<description><![CDATA[Suport teoretic: Schimbarea de variabila&nbsp;si metoda integrarii prin parti la integrala nedefinita.Enunt:Sa se calculeze pe intervalul (0, +00) integrala:$latex I=##int{##sqrt{x+##sqrt{x+1}}}{dx}.$Raspuns:$latex I={##frac{2}{3}}##cdot{(x+##sqrt{x+1})}^{##frac{3}{2}}$$latex +{##frac{1}{4}}##cdo...]]></description>
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					<pubDate>Thu, 01 Dec 2011 20:19:00 +0200</pubDate>
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