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== Intro - Primitiva funktionen ==


Gissa och öva.
== [[Derivatan av y = e^x]] ==


Fundera över det inversa sambandet
== [[Naturliga logaritmer]] ==
== [[Derivatan av 2^x]] ==


Öva på [http://olleh.se/start/frageprogramMa3.php OlleH]
== [[Problemlösning exponentialfunktioner]] ==


{{flipped|'''Till nästa gång:''' se filmen om Riemannsumma}}
== [[Primitiva funktioner]] ==


== Intro - Riemannsumma ==
== [[Beräkna integraler]] ==
== [[Arean av ett område mellan två kurvor]] ==


{{#ev:youtube|lPOUB0fLuUk|340|right|Integral - Riemannsumma}}
== [[Mer om integraler]] ==
== [[Tillämpningar av integraler]] ==


Kan man tänka sig någon trevlig frågeställning som ingång till integralerna?
== Newtons Integralbevis ==


Börja med att visa Riemannsumman för att ta reda på arean under en graf.
<html>
{{clear}}
<script type='text/javascript' src='http://demonstrations.wolfram.com/javascript/embed.js' ></script><script type='text/javascript'>var demoObj = new DEMOEMBED(); demoObj.run('NewtonsIntegrabilityProof', '', '549', '620');</script><div id='DEMO_NewtonsIntegrabilityProof'><a class='demonstrationHyperlink' href='http://demonstrations.wolfram.com/NewtonsIntegrabilityProof/' target='_blank'>Newton's Integrability Proof</a> from the <a class='demonstrationHyperlink' href='http://demonstrations.wolfram.com/' target='_blank'>Wolfram Demonstrations Project</a> by Michael Rogers</div>
 
</html>
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=== Övning Riemannsumma i GGb===
 
{{uppgruta|laborera själv i Geogebra
 
Denna GGB ger dig möjlighet att flytta stapeln och att testa olika funktioner.
 
Du kan ändra på antalet staplar och se hur det påverkar beräkningen.
 
[http://www.geogebratube.org/student/m14091 Här är GGB:n:]
 
Vad lärde du dig av denna övning?}}
 
=== uppg 2 ===
 
Testa denna: http://www.geogebratube.org/student/m11330
 
Hur hanteras negativa areor?
 
=== Uppg 3 ===
 
Man kan skapa Riemannsummor mellan två funktioner:
 
* http://www.geogebratube.org/student/m26214
* http://www.geogebratube.org/student/m26213
 
== Mer om integraler ==
 
{{#ev:youtube|OAN8qa-pnIo|340|left}} {{#ev:youtube|i8JPiQ3Ujyc|340|right}}
 
{{clear}}
 
[http://www.proofwiki.org/wiki/Fundamental_Theorem_of_Calculus ProofWiki]
 
== Mekaniken ==
 
Jämför med mekaniken, sträckan är arean under en vt-graf.
 
== problemlösning med integraler ==
 
{Ma3C|229-232{}

Nuvarande version från 18 april 2016 kl. 22.02