https://3.vobs.at/maturawiki/index.php?action=history&feed=atom&title=Inhalt%3AIntegration%3A_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven Inhalt:Integration: Berechnung von Flächen zwischen zwei Kurven - Versionsgeschichte 2026-10-24T16:15:58Z Versionsgeschichte dieser Seite in Matura Wiki MediaWiki 1.25.3 https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=8197&oldid=prev Simon.Schnetzer: /* Wiederholung und Herleitung der Formel */ 2021-01-28T12:05:50Z <p>‎<span dir="auto"><span class="autocomment">Wiederholung und Herleitung der Formel</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 28. Januar 2021, 12:05 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="L1" >Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Wiederholung und Herleitung der Formel==</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Das folgende Video bietet dir einen Überblick über das Gelernte und erklärt dir die Formel für die Fläche zwischen <ins class="diffchange diffchange-inline">$</ins>2<ins class="diffchange diffchange-inline">$ </ins>Kurven:</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Das folgende Video bietet dir einen Überblick über das Gelernte und erklärt dir die Formel für die Fläche zwischen 2 Kurven:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;br&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;br&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key dbmaturawiki:diff:version:1.11a:oldid:8152:newid:8197 --> </table> Simon.Schnetzer https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=8152&oldid=prev Simon.Schnetzer: /* Übungs- und Lernlinks */ 2021-01-24T16:46:00Z <p>‎<span dir="auto"><span class="autocomment">Übungs- und Lernlinks</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 24. Januar 2021, 16:46 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="L198" >Zeile 198:</td> <td colspan="2" class="diff-lineno">Zeile 198:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://www.brinkmann-du.de/mathe/gost/int_01_05.htm Erklärungen und Beispiele von brinkmann-du]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://www.brinkmann-du.de/mathe/gost/int_01_05.htm Erklärungen und Beispiele von brinkmann-du]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://matheguru.com/30-flaeche-zwischen-funktionen.html Erklärung von matheguru]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://matheguru.com/30-flaeche-zwischen-funktionen.html Erklärung von matheguru]</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [http://<del class="diffchange diffchange-inline">nibis.ni.schule</del>.de<del class="diffchange diffchange-inline">/~lbs-gym</del>/AnalysisTeil1pdf/FlaechezwischenGraphen.pdf Beispiele <del class="diffchange diffchange-inline">samt </del>Lösungen von <del class="diffchange diffchange-inline">Roolfs</del>]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* [http://<ins class="diffchange diffchange-inline">groolfs</ins>.de/AnalysisTeil1pdf/FlaechezwischenGraphen.pdf Beispiele <ins class="diffchange diffchange-inline">mit </ins>Lösungen von <ins class="diffchange diffchange-inline">Groolfs</ins>]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=-6vRkqsQvM4 Weiteres Lernvideo, in dem ein Beispiel vorgerechnet wird]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=-6vRkqsQvM4 Weiteres Lernvideo, in dem ein Beispiel vorgerechnet wird]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key dbmaturawiki:diff:version:1.11a:oldid:8151:newid:8152 --> </table> Simon.Schnetzer https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=8151&oldid=prev Simon.Schnetzer: /* Wiederholung und Herleitung der Formel */ 2021-01-24T16:38:09Z <p>‎<span dir="auto"><span class="autocomment">Wiederholung und Herleitung der Formel</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 24. Januar 2021, 16:38 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="L41" >Zeile 41:</td> <td colspan="2" class="diff-lineno">Zeile 41:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div># Bei dieser Formel ist es egal, ob die Fläche oberhalb oder unterhalb der $x$-Achse ist.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div># Bei dieser Formel ist es egal, ob die Fläche oberhalb oder unterhalb der $x$-Achse ist.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\int_a^b f(x)dx-\int_a^b g(x)dx$$&lt;br&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$\int_a^b f(x)dx-\int_a^b g(x)dx$$&lt;br&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Grün: Arbeitsblätter | &lt;span style=&quot;background-color:#00CD00&quot;&gt; $Aha!$ &lt;/span&gt;]] <del class="diffchange diffchange-inline"> </del>Dies kannst du im [http://tube.geogebra.org/m/194563 folgenden Applet] überprüfen.&#160; &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Grün: Arbeitsblätter | &lt;span style=&quot;background-color:#00CD00&quot;&gt; $Aha!$ &lt;/span&gt;]] <ins class="diffchange diffchange-inline">$\ $ </ins>Dies kannst du im [http://tube.geogebra.org/m/194563 folgenden Applet] überprüfen.&#160; &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1000&quot; height=&quot;478&quot; version=&quot;4.2&quot; id=&quot;194563&quot; /&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1000&quot; height=&quot;478&quot; version=&quot;4.2&quot; id=&quot;194563&quot; /&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr> </table> Simon.Schnetzer https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=8150&oldid=prev Simon.Schnetzer: /* Wiederholung und Herleitung der Formel */ 2021-01-24T16:37:26Z <p>‎<span dir="auto"><span class="autocomment">Wiederholung und Herleitung der Formel</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 24. 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&quot; 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https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=8149&oldid=prev Simon.Schnetzer: /* Wiederholung und Herleitung der Formel */ 2021-01-24T16:36:57Z <p>‎<span dir="auto"><span class="autocomment">Wiederholung und Herleitung der Formel</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 24. 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color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 28. Dezember 2018, 14:11 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="L201" >Zeile 201:</td> <td colspan="2" class="diff-lineno">Zeile 201:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://matheguru.com/30-flaeche-zwischen-funktionen.html Erklärung von matheguru]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://matheguru.com/30-flaeche-zwischen-funktionen.html Erklärung von matheguru]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://nibis.ni.schule.de/~lbs-gym/AnalysisTeil1pdf/FlaechezwischenGraphen.pdf Beispiele samt Lösungen von Roolfs]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [http://nibis.ni.schule.de/~lbs-gym/AnalysisTeil1pdf/FlaechezwischenGraphen.pdf Beispiele samt Lösungen von Roolfs]</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=-6vRkqsQvM4 <del class="diffchange diffchange-inline">weiters </del>Lernvideo in dem ein Beispiel vorgerechnet wird]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.youtube.com/watch?v=-6vRkqsQvM4 <ins class="diffchange diffchange-inline">Weiteres </ins>Lernvideo<ins class="diffchange diffchange-inline">, </ins>in dem ein Beispiel vorgerechnet wird]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--</div></td></tr> <!-- diff cache key dbmaturawiki:diff:version:1.11a:oldid:6917:newid:6918 --> </table> Simon.Schnetzer https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=6917&oldid=prev Simon.Schnetzer: /* Beispiele */ 2018-12-28T14:08:03Z <p>‎<span dir="auto"><span class="autocomment">Beispiele</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 28. 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Dezember 2018, 14:06 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="L123" >Zeile 123:</td> <td colspan="2" class="diff-lineno">Zeile 123:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Besteht eine Fläche aus mehreren Teilschnittflächen, so muss in der Regel jede einzeln berechnet werden.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Besteht eine Fläche aus mehreren Teilschnittflächen, so muss in der Regel jede einzeln berechnet werden.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Dies muss in Beispielen wie dem Folgenden berücksichtigt werden:</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Dies muss in Beispielen wie dem Folgenden berücksichtigt werden:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key dbmaturawiki:diff:version:1.11a:oldid:6915:newid:6916 --> </table> Simon.Schnetzer https://3.vobs.at/maturawiki/index.php?title=Inhalt:Integration:_Berechnung_von_Fl%C3%A4chen_zwischen_zwei_Kurven&diff=6915&oldid=prev Simon.Schnetzer: /* Beispiele */ 2018-12-28T14:05:20Z <p>‎<span dir="auto"><span class="autocomment">Beispiele</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 28. Dezember 2018, 14:05 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="L80" >Zeile 80:</td> <td colspan="2" class="diff-lineno">Zeile 80:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$A_{ \Box&#160; }=a<del class="diffchange diffchange-inline">*</del>a=4<del class="diffchange diffchange-inline">*</del>4=16$&lt;br /&gt;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$A_{ \Box&#160; }=a<ins class="diffchange diffchange-inline">\cdot </ins>a=4<ins class="diffchange diffchange-inline">\cdot </ins>4=16$&lt;br /&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Alternativ kann man hier auch das bestimmte Integral verwenden:</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Alternativ kann man hier auch das bestimmte Integral verwenden:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$A_{ \Box&#160; }=\int_{-2}^2 g(x)dx=\int_{-2}^2 4dx=\left[ 4x\right]_{-2}^2=4\cdot 2-\left[ 4\cdot (-2)\right]=\underline{16}$$</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; 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border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$A=A_{ \Box&#160; }-A_{\cup}=\int_{-2}^2 g(x)dx-\int_{-2}^2 f(x)dx$$</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>$$A=A_{ \Box&#160; }-A_{\cup}=\int_{-2}^2 g(x)dx-\int_{-2}^2 f(x)dx$$</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$$A=16-5<del class="diffchange diffchange-inline">,</del>33=\underline{\underline{10<del class="diffchange diffchange-inline">,</del>67} }$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$$A=16-5<ins class="diffchange diffchange-inline">.</ins>33=\underline{\underline{10<ins class="diffchange diffchange-inline">.</ins>67} }$$</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Wichtig:''' Da hier der Graph von $g$ oberhalb von $f$ liegt, muss man die Formel wie hier gezeigt anschreiben.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''Wichtig:''' Da hier der Graph von $g$ oberhalb von $f$ liegt, muss man die Formel wie hier gezeigt anschreiben.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key dbmaturawiki:diff:version:1.11a:oldid:6914:newid:6915 --> </table> Simon.Schnetzer