[justify]Integralrechnung dient der Ermittlung von Flächenbilanzen oder der Flächenberechnung zwischen einem Graphen einer Funktion und der x-Achse sowie der Strecken- und Massenberechnung.[br][br]In dem folgenden Projekt beschäftigen wir uns mit den [b]Rechenregeln[/b] [b]von Integralen[/b] aus dem "[i]Skript Anallysis 1 und Lineare Algebra für Ingenieurswissenschaften"[/i] (Kap. 30.2, S.238, Oktober 2018). Wir berücksichtigen in diesem Prokjekt nicht die tatsächlichen Flächen, sondern nur die Flächenbilanzen. Das bedeutet, dass negative Flächen mit positiven verrechnet werden, also gilt [b]F (b) - F(a)[/b].[br][br][/justify]
[justify][br][img]data:image/png;base64,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[/img][br][br]Das[color=#6aa84f] [b][color=#000000]Applet 1[/color][/b][/color] zeigt uns die Cosinus-Funktion und die dazugehörige Fläche des Integrals in den Intervallgrenzen [a,b] = [-3,3]. Die "Allgemeine Vereinbarung" besagt, wenn wir ein Integral mit gleicher oberer und unterer Integrationsgrenze berechnen, so ergibt der Flächeninhalt Null. [br][/justify]
[b][color=#3c78d8]Forscher*innenauftrag 1 - Allgemeine Vereinbarung[/color][/b][br]Erforsche diesen Sachverhalt und schiebe die Schieberegler a und b an Applet 1 an einer beliebigen Stelle genau übereinander. Was zeigen dir die Flächenbilanzen an den unterschiedlichen Stellen?
[i][color=#38761D]Genau, das Ergbnis ist an jeder Stelle, an der die Integrationsgrenzen gleich sind, also in der Grafik übereiander liegen, gleich Null![/color][/i][br][br]Auch die Beispielrechnung zeigt, dass Integrale mit gleichen Integrationsgrenzen Null ergeben:[br] [br] [img]data:image/png;base64,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[/img][br][color=#444444][br]Hier noch mal kurz für Dich die Anleitung zum Integrieren:[br]1. Stammfunktion bilden [img]data:image/png;base64,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[/img][br][br]2. Einsetzen der oberen Grenze b, dann das Integral mit der eingesetzten unteren Grenze a davon[br] abziehen[b] F (b) - F(a[/b]). Achtung: Klammern beim Subtrahieren um F(a) setzen, da sich das Minus auf das[br] gesamte F(a) bezieht[/color].
[color=#3c78d8][b]Forscher*innenauftrag 2 - Allgemeine Vereinbarung[/b][/color][br]Wir wissen, dass wir die Fläche zwischen unserem Funktionsgraphen und der x-Achse mit Rechtecken approximieren (Riemannsche Summe) und die Summe aller Flächenrechtecke uns nahezu den exakten Wert des [br]Flächeninhaltes liefert. Versuche mit diesem Wissen den Sachverhalt geometrisch zu erklären.
[i][color=#134F5C][color=#38761D]Woran das liegt? Bei einem Integral mit gleichen Integrationsgrenzen betrachten wir aus geometrischer Sicht im Grunde ein Rechteck ohne Seitenlängen, also einen Balken, der lediglich eine Höhe, aber keine Breite und deshalb auch keine Fläche hat.[/color][/color][/i]
[br][img]data:image/png;base64,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[/img][br][br]Bei einem bestimmten Integral ist die obere Integrationsgrenze [b]b[/b] immer kleiner als die untere[b] a[/b]. Wenn jetzt aber [b]a < b[/b], dann besagt diese Rechenregel, dass wir vor das Integral ein [b]Minus-Zeichen[/b] setzen müssen, um die richtige Flächenbilanz zu erhalten. Allgemein gilt [b]F(a) - F(b)[/b].[br][br]Wir überprüfen das formal:[br][b] [br] F(a) - F(b)[br] = -F(b) + F(a)[br] = -(F(b) - F(a)) = -[/b][math]\int[/math][b]f(x)[br][br][/b]Das Umstellen der Formel zeigt, dass diese Rechenegel rechnerisch korrekt ist. Sie ist sehr wichtig und bildet die Grundlage für die nächste Rechenregel, die Linearität, auch Produktregel gennant.
[br][br][img]data:image/png;base64,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[/img][br][br]Wenn eine gegebene Funktion f(x), wie in [b]Applet 2[/b], einen konstanten Faktor [math]\lambda[/math] enthält - hier unsere Funktion [math]\lambda[/math]*g(x) - ist es erlaubt diese Konstante vor das Integral zu ziehen. Man kann dies mit dem Ausklammern einer Konstante Vergleichen. Diese Regel wird auch [b]Produktregel [/b]genannt.[br][br]
[color=#3c78d8][b]Forscher*innenauftrag 1 - Linearität (Produktregel)[/b][/color][br]Schau dir die Funktion f(x) an und ermittle mit den Schiebereglern die Flächenbilanz im Intervall [-3,3]. Jetzt verschiebe den Schieberegler um einzelne positive oder negative Zahlenwerte. Notiere dir die einzelnen Werte [br]und vergleiche sie untereinander. Was fällt dir bei den Werten der Flächenbilanzen auf?
[i][color=#38761D]Genau, unsere Konstante verursacht nichts anderes als ein Vielfaches eines Flächenwertes. Das ist der Grund, weswegen wir die Konstante vor das Integral ziehen dürfen, um sie zum Schluss mit unserem Ergebnis [br]unserer Integration zu multiplizieren.[/color][/i]
[size=150][size=100][size=100][color=#3c78d8][b]Forscher*innenauftrag 2 - Linearität (Produktregel)[/b][/color][br]Überprüfe die Eigenschaft der Linearität von Integralen mit Hilfe der Produktregel rechnerisch. [/size][/size][size=100][size=100] [br]Berechne das unten stehende Integral auf zwei Lösungswegen: Bei der 1. Rechnung integrierst Du das gesamte Integral, bei der 2. Rechnung ziehst du den Faktor vor das Integral und multiplizierst ihn zum Schluss mit Deinem Ergebnis.[br][/size][/size][/size][size=100][size=100][color=#1155Cc][br]Berechne[/color]:[br] [img]data:image/png;base64,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[/img][/size][/size]
[br][color=#38761D][i]Lösungsweg 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[/img][br][size=50](Die unterschiedlichen Werte aus Lösungsweg 1 und 2 lassen sich auf Rundungsfehler durch die Nachkommastellen zurückführen.)[/size][br][br]Gerade bei der partiellen Integration können so Rechenwege deutlich erleichtert werden.
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[/img][br][br][size=100]Die abgebildete Rechenregel beschreibt die "[i]Linearität[/i]" von bestimmten Integralen. Das bedeutet, dass man ein Integral mit einer Summe in zwei einzelne Integrale aufsplitten und diese nach dem einzelnen Integrieren addieren darf. Gleiches gilt bei einer Subtraktion. Diese Regel wird daher auch als [b]Summenregel [/b]bezeichnet.[/size]
[size=100][color=#3c78d8][b]Forscher*innenauftrag 1 - Linearität (Summenregel)[/b][/color][br]Das [b]Applet 3[/b] zeigt Dir die Funktionen f(x), g(x) und h(x). [size=100]Die Summe aus den Funktionen f(x) und g(x) ist h(x). [/size][br][br]Blende die Funktion h(x) ein und ermittle die Flächenbilanz im Intervall von [-3,3]. [br][br][/size][size=100]Gemäß der Rechenregel, dass die beiden einzeln integrierten Funktionen f(x) und g(x) die gleiche Flächenbilanz ergeben blende nun h(x) aus und ermittle die beiden Flächenbilanzen von f(x) und g(x). Addiere beide Flächenbilanzen und vergleiche das Ergebnis mit der Flächenbilanz von h(x). Was hast du herausgefunden?[/size]
[size=100][color=#38761D][i]Genau[/i], es kommt bei der rechnerischen Ermittlung der Flächenbilanzen immer das gleiche raus![br]Wir konnten durch die Berechnung mittels geogebra feststellen, dass diese Rechenregel gilt.[/color][/size]
[size=100][size=100][b][color=#3c78d8]Forscher*innenauftrag 2 - Linearität (Summenregel)[/color][/b][br]Überprüfe die Eigenschaft der Linearität von Integralen rechnerisch. Berechne mit Hilfe der Summenregel das unten stehende Integral auf beiden Lösungswegen. D.h. zuerst integrierst Du das gesamte Integral, das zweite Mal splittest du die Summe in zwei Einzelintegrale auf. Du kannst Dich selbst überprüfen, denn beide Ergebnisse müssen gemäß der Summenregel übereinstimmen.[br][br][color=#1155Cc]Berechne:[/color][br] [img]data:image/png;base64,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[/img][/size][/size]
[size=100][size=100][color=#38761D][i]Lösungsweg 1[/i]: [br][img]data:image/png;base64,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[/img][br][br][i]Lösungsweg 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[/img][/color][br][br][i][color=#38761D]Diese Rechenregel ermöglicht es uns übrigens auch unterschiedliche Integrale ohne oder mit gleichen Integrationsgrenzen zu einem Integral zusammen zu ziehen. Das kann uns den Rechenaufwand beim Integrieren deutlich vereinfachen.[/color][/i][/size][/size]
[br][img]data:image/png;base64,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[/img][br][br]Diese Rechenrgel besagt, wenndie[b] Funktion f(x) kleiner/ gleich g(x)[/b] für alle x Element [a,b], [br]dann ist auch das berechnete Integral bzw. die [b]Fläche von f(x) kleiner/ gleich g(x)[/b].
[color=#3c78d8][b]Forscher*innenauftrag 1 - Monotonie[/b][/color][br]Um das zu verstehen, betrachte in [b]Applet 4[/b] die Funktion k(x) = ln(x) und die Flächenbilanz im Intervall von [1,8], ln(x) ˃ 0. Checke nun die Flächenbilanz von h(x)=λ [math]\frac{1}{2}x[/math] im gleichen Intervall mit λ ˃1.[br]Wie verhalten sich die Flächenbilanzen beider Funktionen zueinander?[br]
[color=#38761D][i]Genau[/i], es liegt Monotonie vor, denn k(x) ≤ λ*h(x) und damit ist die Fläche [/color][color=#38761D][color=#38761D]zwischen der Funktion [color=#38761D]k(x)[/color] und der x-Achse im angegbenen Intervall[/color][/color][color=#38761D] [color=#38761D]≤ h(x)[/color].[/color][br] [img]data:image/png;base64,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[/img][br]Wir können dies folgendermaßen begründen, indem wir g(x)= [math]\frac{1}{2}x-ln\left(x\right)[/math]nehmen. Die Differenz zwischen h(x)=[math]\frac{1}{2}x[/math]und k(x)=ln(x) ist immer größer 0. Das bedeutet, dass k(x) kleiner h(x). [br]Damit ist Die Differenzenfunktion g(x) das Argument für diese Regel.
[b][color=#1e84cc]Forscher*innenauftrag 2 - Monotonie[/color][/b][br]Was passiert, wenn Du den Schieberegler für λ in Applet 4 in den negativen Bereich verschiebst?
[color=#38761D][i]Genau, jetzt ist λ*h(x) kleiner/ gleich k(x) und damit wird auch die Flächenbilanz von λ*h(x) kleiner als die von k(x). Das liegt natürlich auch daran, das ln(x) nicht für negative Zahlen definiert ist.[/i][br][br][/color]
[br][img]data:image/png;base64,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[/img][br][br]Die Rechenregel "[i]Dreiecksungleichung[/i]" besagt, dass es einen Unterschied macht, ob wir das gesamte Integral oder nur die Funktion in Betrag nehmen. Das in Betrag gesetzte Integral ist immer [math]\le[/math] als die in [br]Betrag gesetzte Funktion.[br][br][img]data:image/png;base64,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[/img][size=50][br]Quelle: Skript Mathematik für Ingenieure[/size] [size=50]Uni Kiel[/size][br][br]Beim Integral auf der linken Seite (Abb. links) werden die beiden äußeren Flächen positiv gezählt und die mittlere Fläche wird abgezogen, und die entstehende Summe ist kleiner als die Summe aller drei positiv gerechneten Flächen auf der rechten Seite (Abb. rechts). Dies begründet eigentlich nur [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMUAAAAcCAYAAADRCXsXAAAOpklEQVR4Xu2cfVzP9/rHn27Xbxpjczs8pjkty0+ObLWjDtWPitzVLJTcVphaydzsGMcmQhiyNTfpVhrVKFvxKzflYGNH5iYkjijKzTjlSOVzPt8b9VXfvnd9fW2P9f3L4+Hz/nyuz/W6Xu/rfb2u61MTQfyh5U8oOsSa+QsIbruYvC8daafl+qeXPynI5Ouob9m1Io4bzjPwcfNgursFxjre73exrLKQY9FbSbjQDNPepnR8+T/cyj3PNaMBTPZ1wtS4mV5eQ18Y6cWY39lNmuhCCrjPseAxhHT/iuQJPWnyO3vpP4a5jRjpirNupHiSS4TzQh6vjWb6Oy/r+uzGdc/TA40Y6exdnUghFCUxxfRzygJn4GJ0lp/e9meNW09a6GxG40J9e6ARI909qpIUQkk2Xy5Lx8jqLcpy/k0/fx/sO7ekLGsJvTf+iYzY8ZiUJDPR6jTTzi/GtlXjQUp3KHRb2YiRbn5Ttap+UggFpH40jb1DI/hqQC7zrSbwj9n7ODjdhAvhE/Blifjv3jS5GIGz5Sn88tfi0l4fRWI5RZlb+KbEgfnuZhhp9M4Cjy4mEpLSDt+P7ejc/A9CTn1gVJXDepfDDEz1w6JB8OmCmwjuo1wSQjJo7ztN3HBfqou23uzTKJCkF9VLCuFaAh7mKTif3sqEN+9zMn4/t61H4Whyn9TpU/nRI47PbVtTnDqHvlstyU6cgElTDR5ceZ3M0I0cfe01/n2nP0HzBtG+OoarKM3ZjH9yL1YvHkhbrWK7intZqwk65cD6WZYYa7NWuE76kvmExO7mYOtgTv3k38AA0cAPerhELxhVniTU+gB2x+Zg2VyFUc8NNxDuHWJJ0HlGr/fGorb6pql91aZXUJS+isCQSBIOvsW6U7vwt2illbfrIUUVJamBmPh1Yn/uAqxfUoyw22TOm8nPH0Ywp99dkqbNJ3faeha8/7oGKtRDLkZ443h1Mvve+55h4ypZo5hhHv7M+gkp9N68EPt2OmxbQjGZny7izNiVoiNaa+UIkLyXE56sJHeFPdqu1vJhNZdXFpOTXUgHGwstM5yeMNIo6J4zblRxN3Mp3meGE+Pfj2ekG43sq+39JzzIXIiZJ8TmLsW+tSa7dc096iFFKSdDh9M/fBgncmvvIJKjSjyfRtyh7+u3udFzHH4jzTTbmR+fYr3dNPIX7WFpt5Nsv2jC+JHm8rUVFCbNZtz1qez370tLnaJM4HFOGIPXvUH8Vle6aJMtqs4QPmgcxwP3EuHaXQOC62Rg9SKh9DIHk+KJjDxFJ88gArystSSFnjDSJOieO26iWyTPGLyVrvFrcO2iINloYl8dKB5yLnw8Vse9xE3Ylc7axEH9x6dC8YjkwPD/BFMYJd60YfhXr34iqT/eTsP9QrSoXtWqFp5cIsbtM8qCIxom80qDexktt0bUfYaK9xCuxDDaJBGns9sb9nyVvhKoLMkhdUc025J/5d1JXni42tJDp4adnjDSIOgMghuSQPYisOVSfphiRvXeroF9dVwu5BEz2olNTt9J615tzxzKM4U0sP7KDJMteiSFmCLT59HT25jdSpQq6fnY/jL+Z2sf17RlpC5NK3m6ndSShOeioom10pUskuKiiTxsxNDpPkwcYUH7hggC+sJIbdAZCjeB8mPLMQvpRmbyBHo83d3V2qckPh5kMs9sIS8lpIp1r/bzFspJUZbFol5/Jcb3KLl/s0aJJqBVpApFWWyOy+DnvRHEMZR5w3pi1G2wwkiHPCij+nOyTmYSd9ei4yTs/InytlWczqxkeNC7XN51gqatcvk234Gwte6YGj31YgUFCb5Y/eypojYQgzQ/g4iwDB73taBtcTG3ru0ktOmimrEVyThGQjI/lotF2ukfKR0+DbvL6RwRt7Cz3xbjGPYFY03VDaSUU5KTxo7IbURdMmNmkDcfDnpLs6OmOg/rCyMVQWdY3MSCuyCBcVY5+CjWARqQQijNY1/EFtIfm/Fe2wfcuXWe8NBWhOatwFFam4rK2LFkdv5YRlvOkVk6hCC7G+w68ohWZ/eT77ictWNrlE7lpBCbcxO7uHFk1Qly51iiSpRQh13NIfoqCeP+jxV/SeQnf4taKa2cKzFTGXjJl/Of2/KMVlBxiZ1hF7DyG0b35mWyWifKnsNHZtNx11SsdwzgwHezsHj5KSkEaR+l1+q3OKS441QbIhLibCx+gZcZG/U3HEUZUChOZabZTIrWZcrHVh6SvzOW01ZejOpuROXJUMz6p+BxOIlFHXfjYi2qcgeiVBbzQskRwuYuJJ5hzAnwYoRFB/348el76AsjdUEnGAo38cWkRP+GPx0SFc8e8q1YjX1C6Wm2+X3OxbFrWerYjebCDVJnOjG8aC75UvwFKvJ3E3a6D36jTGguuZ/ZIKI89nJkUQd2uYxmh3Mc3ykU+EpJIQuCjfTfcYB49zf1U3RKX9iPB5vT+dKxYy0uyYpGd0LrkLDqXDwb7gwhwPY1cc0t0gMc8W69oS55FO4otd8dEuqIBOJFEoVrlA+npiexVV5Qy7q/0WJhJq8nqs4SueEergE2ogql+vhQ76ZQWcSJxBg2rvsBXD8mYKIzFu0bmnMVRCt9YaSOFAbETdx9xICdIwKXwhxLeRZWad8DctZPxPnUBE48FVaEayRNGcZaq3h5PSHWKpHx3HGdjK1EhbqbTkDPJbTeXf/RSgkp5EcZh2RGpGQQ7tJF42Sg6kJZsbaH0UoL2fpJ8cw9VQJUK2CUkqJS2lcx84Lo3FBcOkhyoDyzeECc0nriLlmLXBj5QMeJYInkmp7M9k1JXOnjzowpHzCoR+sGbjR6xEgNKQyJm7akkGX4BSKYaXzl8obMp9IYmSeCqSzo5ViPLGVz9dGqbtQqIUUlRUmz6OJ2gVUnFBjbIGqo041lEtqI0s9UHteqzoUzyDwbn3yF9KrELmmmCDBmz8HpvPOM9CDLNE5Xg+SpVbJY9myb3BnKx+ClBe0o0nzSGjYRLDzgSvb37IqIJvtVZyZPcsdF5yOVHjFSSQrD4iYjxRcY71FQAOu1T57BnW6yTiEepDFik8dCpUEvw9o8zU0Bf41IIV84w5hoNcGnOU/UGSMHefcQFWqXrO4w2WTDWXmwP8lPZF2eDYFDFI9jsnuZ7nMhP9yF9s8YWUDSRDuCTGNrBASpfDecRLcUkkeKDk5qi98k8+qap45UK0rH29ddwynQQcfvSCTFdwZJ2yNIKH4PHzFzuNiYaFl86xEjlaQwJG4iUJI6yfQgYxQbuvXaJ4+ZoO4crW4wy2Mk0VEM+qFcX7eP1/zG1WyMdaTacvK3R5PnNIUhCs1iJZlC3hRaZkmaihSjOSEkV8o0db9u2+pVs6QM93xMmOKIhXS2x43Zryzn+NLOJI8ZxtQ2q2XEEUrIDkuhmedE3m+rmA4kQNbMZj2rUYtOiJmGwyUfzkgLelGVyFiFx6gMhh7cjc/DGDa3+JDxt5czcPb/EH58AV2TfbGc+gpRhWG4il2ge9mRxDYbySyNOviqvCSRaY+SuiuKTf/oz9o4HwWxQJ139YiRSlIYEjeQxoAvfKOY4VXY9yQ/BjeHy8w+IxlGRVQp/58vPKYSNzSZXJ+HhG5ugd/4Ej4ZGMIr4cks7ZrKGMtltIk6QJRrN3G8JJuw2GZ4znpfNlJUeoKvfUKUzT7Jxh0c9nvpbwao/BjBZpMp2KCiRnl4lOC/RNBzz0bcu8v72cJNskKCCP3VCicjUU5zsaUifg+33u2NcSGYj3fHtvYQmXCFBI9ACoKixWKt7rCGRK2Inf81ee/Z0OX6VQQbN2z+9Q2r//Um5m364DHDhuZH1+EdWoKj0yvcbGuHS8X3bL/1Nv2M71Nh7oqX7Rv6VZLUcaDO/+sRI1WkMCRuPOZawkeMKvDl6Jz+NW0AVfYJ9zkbG8zqvLcZ0qWE84I1XjYFLFudj6V5F8w8vLBrfowQ74386miL0c32uLhUEL+9mHf7taKwojfjvQZUTxIIJWnMHjBGGSlkRww3cQZIsZstDaZF2ygwf5Pyq8U8auPE/Dm2ou6r/ic7gqQwQlknu3q5OHQY6s1Gk9BqVUj9neteIRQmMXXcDT7eL8q0LbXs7+vywBeyRo8YqepTGBA3JKrR1Plc/3iTKHUr9H/UqWN693+pElJIv9iyZ9nglJqiV+wVJPgu5rJPGAusjTgvFitOhUEqZVFEFl/8fi/nejhhdzOU/93Qi4NqJmklAT3N71fm7ZiMaQtdAloyuBbAilcXssUA80t6x0PTG+oLI8nzagfdC8FN7CVc3MbYFa+yYUutmTVDk0I8adStKaSSViDlkWmssH9d9JqoQGR9gdX8duw4INl9i0UFZwI/OMco6TcooFqSynSTv9M0XlSKclay+/21LLfvoEaKFJtmCcFsefUjgh27aClbip3va7uZu/Ixs9aOwUQnUmkaleqvE4rSWfLpdq48UX8treyYHTpR85pCXxgpI4XBcZMQ8wpJczdRMesz3E1qfd5sYFII176TkOK2kLVoFEN/8SEn0ZOuv4Rh513G6sy5WBtLxrLKxAbJBzjf+EQ2NlF+glCrUNp9G8bQ1kZ07GSsPHjFeuDwmq2catOEq3cHsOCTgQrfTagIFHFuP2NVJDfdAvBQO0ahcJ9H54hbso9O/jNwUPaxigax+du95I7YK3kOGCnNFAbGjVIuxn1JYqdJfOLQtW6tZkhSiN/V7PvqhIQUZUJ+wlw8DzmyK8SU7MUryPtwpcL3ETKZa/CtQPE41ZdHJzcw4oOHBO81IfUXK5a699ByR9cg9MSG1+lzFfTq84aG332L6ff6Oc6/1JM+euwaa2CpgS6RZNDnhJF4XLr0z9t0/rMeZrK0xk10X8UNTp9vwTt96hmD0ad9GqIlPz5JtPMsjlyBHgNs64wjCPeOsjpoD60GdaXscVMeJB2jXJyidZk8Edv2epmM0tDcP/JljRgZCn2d/pqHoYxrfE6jB16EBxpJ8SK83vjM37QHGknxm4an0bgX4YH/Asy+J396InLCAAAAAElFTkSuQmCC[/img], aber bei [img]data:image/png;base64,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[/img] werden die beiden äußeren von der mittleren Fläche abgezogen, und wir haben wieder dieselbe Ungleichung. Dies lässt sich formal mit der Rechenregel 2 [b]Monotonie [/b]herleiten.[br][color=#3c78d8][b][br]Forscher*innenauftrag 1 - Dreiecksungleichung[/b][/color][br]Erforsche diesen Sachverhalt der Dreiecksungleichung am [b]Applet 5[/b]. Achte darauf, dass du die Regler der Integrationsgrenzen gemäß oberer und unterer Integrationsgrenze richtig wählst. Beim Applet bedeutet das, dass die untere Integrationsgrenze a immer größer als b sein muss. Schau Dir die Flächenbilanzen von c und d an. Laut Rechenregel muss c kleiner/ gleich d sein. Überprüfe diesen Sachveralt.
[color=#3c78d8][b]Forscher*innenauftrag 2 - Dreiecksungleichung[/b][/color][br]Stimmt das denn in jedem Fall? Was passiert, wenn wir die Integrationsgrenzen vertauschen?[br]Vertausche die Integrationsgrenzen und schau dir das Flächenverhältnis von [color=#BF9000][b]c[/b][/color] zu [color=#0000ff][b]d[/b][/color] an. Was stellst du fest?[br][br]Nach unserer Regel müsste doch [color=#BF9000][b]c[/b][/color] [b]kleiner/ gleich[/b] [color=#0000ff][b]d[/b][/color] sein.[br][br][b]Tipp[/b]: Lässt sich hier vielleicht eine Beziehung zu Integrationsregel 2 [b]für a [/b][b]< [/b][b]b[/b] herstellen?[br][br]
[i][color=#38761D]Genau, wenn wir die Integrationsgrenzen vertauschen, dann haben wir das Problem, dass unsere in Betragsstriche genommene Funktion f(x) (im Applet unser d) negativ wird. Die Relation der Dreiecksungleichung dreht sich um und scheint nicht mehr gültig: [/color][/i][i][color=#38761D][color=#BF9000][b]c[/b][/color] [color=#0000ff][b][color=#000000]größer/ gleich[/color] d[/b][/color]. [br][br]Die Dreiecksungleichung ist aber doch gültig und die Begründung hierfür liefert uns wiederum Rechenregel 2 [b]für a [/b][b]< [/b][/color][/i][i][color=#38761D][b]b[/b]: Für den Fall, dass die Integrationsgrenzen vertauscht werden, müssen wir vor das in Betragsstriche gesetzte Integral ein [b]Minuszeichen [/b]setzen: [/color][/i][br][br] [img]data:image/png;base64,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[/img][br][color=#38761D]Jetzt stimmt Relation der Dreiecksungleichung wieder![/color]