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Zuletzt geändert von Holger Engels am 2025/12/17 06:52
Von Version 6.1
bearbeitet von kickoff kickoff
am 2023/10/09 13:08
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Auf Version 20.1
bearbeitet von Holger Engels
am 2025/12/17 06:51
Änderungskommentar: Neues Bild Gefäß.svg hochladen

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Dokument-Autor
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1 -XWiki.kickoff
1 +XWiki.holgerengels
Inhalt
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1 +{{seiteninhalt/}}
2 +
1 1  [[Kompetenzen.K1]] Ich kann das bestimmte Integral als rekonstruierten Bestand deuten
2 2  [[Kompetenzen.K1]] Ich kann das bestimmte Integral als Flächeninhalt zwischen Funktionsgraph und x-Achse deuten
3 3  [[Kompetenzen.K5]] Ich kann den Wert bestimmter Integrale mittels Flächenzerlegung näherungsweise ermitteln
4 -[[Kompetenzen.K5]], [[Kompetenzen.K6]] Ich kann den propädeutischen Grenzwertbegriff beim Übergang von Unter- und Obersummen zum bestimmten Integral nutzen {{niveau}}e{{/niveau}}
6 +[[Kompetenzen.K5]] [[Kompetenzen.K6]] Ich kann den propädeutischen Grenzwertbegriff beim Übergang von Unter- und Obersummen zum bestimmten Integral nutzen {{niveau}}e{{/niveau}}
5 5  [[Kompetenzen.K6]] Ich kann den Wert eines bestimmten Integrals als Bilanz orientierter Flächeninhalte interpretieren
6 6  [[Kompetenzen.K6]] Ich kann die Eigenschaften des bestimmten Integrals erläutern {{niveau}}e{{/niveau}}
7 -[[Kompetenzen.K5]], [[Kompetenzen.K6]] Ich kann die Eigenschaften des bestimmten Integrals nutzen {{niveau}}g{{/niveau}}
9 +[[Kompetenzen.K5]] [[Kompetenzen.K6]] Ich kann die Eigenschaften des bestimmten Integrals nutzen {{niveau}}g{{/niveau}}
8 8  
9 -== Deutung des bestimmten Integrals ==
11 +{{lernende}}
12 +Siehe dazu [[Rekonstruktion einer Größe>>https://kmap.eu/app/browser/Mathematik/Integralrechnung/Rekonstruktion%20einer%20Gr%C3%B6%C3%9Fe]] und [[Obersumme/Untersumme interaktiv>>https://kmap.eu/app/browser/Mathematik/Integralrechnung/Obersumme%20und%20Untersumme#erkunden]]
13 +{{/lernende}}
10 10  
11 -== Näherungsweise Berechnung von Integralen mittels Flächenzerlegung ==
12 -
13 -{{aufgabe afb="II" kompetenzen="K5,K6" quelle="Jonathan Weis" cc="BY-SA" niveau="e" zeit="7"}}
14 -Gegeben ist die Funktion f mit {{formula}}f(x)=\frac{1}{4}x^2+1{{/formula}}. Gesucht ist der Flächeninhalt der Fläche zwischen dem Funktionsgraphen und der {{formula}}x{{/formula}}-Achse im Intervall {{formula}}[0;4]{{/formula}}.
15 +{{aufgabe id="Gefäß" afb="I" kompetenzen="K4" quelle="[[KMap>>https://kmap.eu/app/browser/Mathematik/Integralrechnung/Rekonstruktion%20einer%20Gr%C3%B6%C3%9Fe]]" zeit="5"}}
16 +**Aufgabenentwurf**
17 +Ein Gefäß sei zu Beginn der Beobachtung mit //10 l// gefüllt. Es wird folgender Zufluss/ Abluss beobachtet:
18 +[[image:Gefäß.svg]]
19 +Bestimme den Füllstand nach diesen Veränderungen.
15 15  {{/aufgabe}}
16 16  
17 -== Bestimmtes Integral als Grenzwert einer Summe ==
18 -
19 -== Orientierter Flächeninhalt ==
20 -
21 -== Eigenschaften des bestimmten Integrals ==
22 -
23 -
22 +{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Gefäß.svg
Author
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1 +XWiki.holgerengels
Größe
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1 +22.5 KB
Inhalt
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Untersumme_0.png
Author
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1 +XWiki.kickoff
Größe
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1 +34.8 KB
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Untersumme_1.png
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Untersumme_2.png
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Untersumme_3.png
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Größe
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Untersumme_4.png
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XWiki.XWikiComments[0]
Autor
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1 +XWiki.kickoff
Kommentar
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1 +Soll die Aufgabe 1 durch Flächenzerlegung gelöst werden? Oder passt diese Aufgabe eher zu einer anderen BPE?
Datum
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1 +2023-10-09 15:35:53.47
XWiki.XWikiComments[1]
Autor
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1 +XWiki.kickoff
Kommentar
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1 +Laut BP gehört Ober- und Untersumme zu 13.1, daher hab ichs da mal reingestellt.
2 +Die Aufgabe ist wohl eher als Erarbeitung tauglich.
Datum
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1 +2023-10-09 16:05:56.242
XWiki.XWikiComments[2]
Autor
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1 +XWiki.holgerengels
Kommentar
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1 +Da es eine Erarbeitungsaufgabe ist, habe ich sie hierher verschoben: [[Jahrgangsstufen.BPE_13L.Erarbeitungsaufgabe Untersumme.WebHome]]
Datum
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1 +2025-12-16 06:21:49.534
Antwort an
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1 +1