Newton-Leibnizova formule

[url=https://cs.wikipedia.org/wiki/Z%C3%A1kladn%C3%AD_v%C4%9Bta_integr%C3%A1ln%C3%ADho_po%C4%8Dtu][b]Základní věta integrálního počtu[/b] [/url]udává vztah mezi dvěma základními operacemi [url=https://cs.wikipedia.org/wiki/Integr%C3%A1ln%C3%AD_po%C4%8Det]integrálního počtu[/url]: [url=https://cs.wikipedia.org/wiki/Derivace]derivováním[/url] a [url=https://cs.wikipedia.org/wiki/Integr%C3%A1l]integrováním[/url].[br][br]Pokud je funkce f(x) [url=https://cs.wikipedia.org/wiki/Spojitost]spojitá [/url]na uzavřeném intervalu [a, b], pak [math]\int_a^b f(x) dx = F(b)-F(a) [/math],[br]kde F'(x) =f(x); F(X) je tzv. [url=https://cs.wikipedia.org/wiki/Primitivn%C3%AD_funkce]primitivní funkce[/url] k funkci f(x). Tento vztah bývá též označován jako [i][url=https://cs.wikipedia.org/wiki/Isaac_Newton]Newton[/url]-[url=https://cs.wikipedia.org/wiki/Gottfried_Leibniz]Leibnizova[/url] formule[/i], popř. se o něm také hovoří jako o základní větě integrálního počtu.[br][br]Nejjednodušším integrálem je [url=https://cs.wikipedia.org/wiki/Riemann%C5%AFv_integr%C3%A1l]Riemannův integrál[/url], který vychází z intuitivní představy měření obsahu plochy pod [url=https://cs.wikipedia.org/wiki/Graf_(funkce)]grafem funkce[/url]. Chceme-li přibližně zjistit tento obsah, provedeme to v praxi pravděpodobně tak, že položíme do měřené plochy nějaké útvary, jejichž obsah dovedeme spočíst, tak, aby nepřesahovaly hranici měřené oblasti a vzájemně se nepřekrývaly. Sečteme-li nyní obsahy všech vložených útvarů, dostaneme zřejmě číslo, které je menší než obsah měřené plochy — tzv. [url=https://cs.wikipedia.org/wiki/Doln%C3%AD_odhad]dolní odhad[/url]. Obdobně (pokrytím [b]celé[/b] měřené plochy známými útvary) získáme tzv. [url=https://cs.wikipedia.org/wiki/Horn%C3%AD_odhad]horní odhad[/url].[br]Obsah měřené plochy pak leží mezi dolním a horním odhadem. Budeme-li používat k vykládání plochy stále menší a menší útvary, dokážeme oba odhady stále zpřesňovat, až teoreticky při vyložení plochy [url=https://cs.wikipedia.org/wiki/Nekone%C4%8Dno]nekonečně[/url] mnoha nekonečně malými útvary dostaneme horní i dolní odhad roven stejnému číslu — obsahu měřené plochy.[br]Plocha mezi částí nějaké křivky a vodorovnou osou v rovině obecně není souhrnem ploch konečného počtu pravoúhelníků určených křivkou, ale součtem či integrálem nekonečného počtu obdélníků nekonečně malé [br]šířky.
Riemannův integrál kvadratické funce f(x)
Výpočet derivace funkce a hledání obsahu plochy pod grafem jsou "obrácené" operace. Toto je pointa základní věty integrálního počtu. Většina formálního [url=https://cs.wikipedia.org/wiki/Z%C3%A1kladn%C3%AD_v%C4%9Bta_integr%C3%A1ln%C3%ADho_po%C4%8Dtu#D%C5%AFkaz_prvn%C3%AD_%C4%8D%C3%A1sti]důkazu[/url] věty je věnována existenci primitivní funkce F(x). [br][br][url=https://cs.wikipedia.org/wiki/Gottfried_Leibnitz]Gottfried Leibniz[/url] (1646-1716) odvozoval vztah mezi derivací a integrací na kvadratické a kubické parabole. Vycházel z geometrické představy derivace jako směrnice dy/dx pro nekonečně malé přírustky [color=#0000ff][i]dx[/i][/color] a [i][color=#0000ff]dy[/color][/i]. [br]Označme [color=#0000ff]F(x[sub]0[/sub])[/color] obsah plochy pod grafem funkce [color=#0000ff]f(x)[/color] na intervalu [color=#0000ff](0, x[sub]0[/sub])[/color].[br]Zjednodušeně můžeme Leibnizovy úvahy zapsat, pokud připustíme, že je zelených obdélníků (obrázek výše) nekonečně mnoho, jejich vodorovná strana je nekonečně malá [color=#0000ff][i]dx[/i][/color] a výška má velikost [color=#0000ff]f([i]x[/i])[/color], tj. obsah [color=#0000ff][i]dF[/i][/color] každého z nich je[i][color=#0000ff][center]dF = f(x)[color=#0000ff] . dx[/color][/center][/color][/i]Každý obdélník je rozdílem obsahu plochy [color=#0000ff]F(x)[/color] a [color=#0000ff]F(x+dx)[/color] pro nějakou hodnotu [color=#0000ff][i]x[/i][/color].[br][center] [br][math]F\left(x+dx\right)-F\left(x\right)=f(x)\cdot dx \\[br]\frac{F\left(x+dx\right)-F\left(x\right)}{dx}=f(x) \\[br]\frac{dF}{dx}=f(x)[br][/math][br][/center][br]
Výpočet obsahu plochy pomocí integrálů
Při výpočtu musíme mít představu o znaménkách hodnot funkce. Pokud je na celém intervalu funkce kladná, je určitý integrál rovný přímo obsahu plochy vymezené osou x a grafem funkce. Pro záporné funkce vyjde určitý integrál záporný, obsah je absolutní hodnota určitého integrálu.[br]Pokud na zkoumaném intervalu funkce protíná souřadnicovou osu x, musíme výpočet obsahu plochy rozdělit na dvě části. [br][br][size=150]Obsah plochy mezi funkcemi f(x), g(x)[br][size=100]Nechť např. na celém intervalu je f(x)> g(x). Nejprve spočítáme obsah plochy pod funkcí f(x) a od ní odečteme obsah plochy pod g(x).[br][img]data:image/png;base64,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[/img][/size][/size]
Výpočet obsahu plochy mezi f(x) = sin x a g(x) = cos x.
[code]IntegralBetween(f,g,((pi)/(4)),((5pi)/(4)))[br]IntegralMezi(f,g,((pi)/(4)),((5pi)/(4)))[/code]
Literatura
Kapitola [url=https://matematika.cz/integral]Integrál[/url] na serveru matematika.cz[br][url=http://www.realisticky.cz/ucebnice/01%20Matematika%20S%C5%A0/10%20Diferenci%C3%A1ln%C3%AD%20a%20integr%C3%A1ln%C3%AD%20po%C4%8Det/03%20Integr%C3%A1ln%C3%AD%20po%C4%8Det/13%20V%C3%BDpo%C4%8Det%20plochy%20obrazce%20I.pdf]Výpočet plochy obrazce I[/url], [url=http://www.realisticky.cz/ucebnice/01%20Matematika%20S%C5%A0/10%20Diferenci%C3%A1ln%C3%AD%20a%20integr%C3%A1ln%C3%AD%20po%C4%8Det/03%20Integr%C3%A1ln%C3%AD%20po%C4%8Det/14%20V%C3%BDpo%C4%8Det%20plochy%20obrazce%20II.pdf]Výpočet plochy obrazce II[/url] na serveru realisticky.cz[br]Prezentace k přednášce "[url=https://docs.google.com/presentation/d/e/2PACX-1vTWKj_QqUI_BnbEzuHA4QiNtFfiQsWSswr0F-fz-Su9tjI6ImsObMUv9N3eC8kZxcVE3yh-IwwZ4cE9/pub?start=false&loop=false&delayms=3000]Funkce[/url]", Google Slides[br]Prezentace k přednášce "[url=https://docs.google.com/presentation/d/e/2PACX-1vTM6dAfwJsT8mfnb-ERepICtTl5UBXJAUphGIU8pc2nQY36Yeah7aH_rPxyELZtu4Tu1khC2w9OU7dc/pub?start=false&loop=false&delayms=3000]Infinitesimální počet[/url]", Google Slides
Určitý integrál

Information: Newton-Leibnizova formule