Finding the area between two curves with Integrate The 2019 Stack Overflow Developer Survey Results Are InHow to evaluate this indefinite integral $csc(4x)sin(x)$Finding the centroid of the area between two curvesRevolving the area between two functions about an axisArea enclosed by two functionsComputing the area between two curvesIntegrate to calculate enclosed areaInteresting discrepencies between integrate functionsFinding the volume enclosed by two surfaces of revolutionFinding an area enclosed by 4 curvesApproximate the relationship between 6 nonlinear functions involving elliptic integrals

Why are there uneven bright areas in this photo of black hole?

Mathematics of imaging the black hole

Getting crown tickets for Statue of Liberty

How can I have a shield and a way of attacking with a ranged weapon at the same time?

Can a flute soloist sit?

Pokemon Turn Based battle (Python)

What is the most efficient way to store a numeric range?

Did Scotland spend $250,000 for the slogan "Welcome to Scotland"?

What is the meaning of Triage in Cybersec world?

Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?

How to charge AirPods to keep battery healthy?

Why don't hard Brexiteers insist on a hard border to prevent illegal immigration after Brexit?

Why isn't the circumferential light around the M87 black hole's event horizon symmetric?

How to translate "being like"?

How to type a long/em dash `—`

What does もの mean in this sentence?

Geography at the pixel level

Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?

Accepted by European university, rejected by all American ones I applied to? Possible reasons?

Cooking pasta in a water boiler

Is Cinnamon a desktop environment or a window manager? (Or both?)

I am an eight letter word. What am I?

Can withdrawing asylum be illegal?

Is bread bad for ducks?



Finding the area between two curves with Integrate



The 2019 Stack Overflow Developer Survey Results Are InHow to evaluate this indefinite integral $csc(4x)sin(x)$Finding the centroid of the area between two curvesRevolving the area between two functions about an axisArea enclosed by two functionsComputing the area between two curvesIntegrate to calculate enclosed areaInteresting discrepencies between integrate functionsFinding the volume enclosed by two surfaces of revolutionFinding an area enclosed by 4 curvesApproximate the relationship between 6 nonlinear functions involving elliptic integrals










2












$begingroup$


I'm trying to solve and approximate the area between the two graphs. Right now, my functions are stored as



f[x_] := 3 Sin[x]
g[x_] := x - 1


and then I tried to integrate by evaluating



Integrate[Abs[f[x] - g[x]], x]


Instead of getting an answer, I just get the exact same thing I inputted



Integrate[Abs[f[x] - g[x]], x]


How do I fix this?






calculus-and-analysis







share|improve this question









New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$











  • $begingroup$
    You can format inline code and code blocks by selecting the code and clicking the button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful
    $endgroup$
    – Michael E2
    1 hour ago















2












$begingroup$


I'm trying to solve and approximate the area between the two graphs. Right now, my functions are stored as



f[x_] := 3 Sin[x]
g[x_] := x - 1


and then I tried to integrate by evaluating



Integrate[Abs[f[x] - g[x]], x]


Instead of getting an answer, I just get the exact same thing I inputted



Integrate[Abs[f[x] - g[x]], x]


How do I fix this?






calculus-and-analysis







share|improve this question









New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$











  • $begingroup$
    You can format inline code and code blocks by selecting the code and clicking the button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful
    $endgroup$
    – Michael E2
    1 hour ago













2












2








2





$begingroup$


I'm trying to solve and approximate the area between the two graphs. Right now, my functions are stored as



f[x_] := 3 Sin[x]
g[x_] := x - 1


and then I tried to integrate by evaluating



Integrate[Abs[f[x] - g[x]], x]


Instead of getting an answer, I just get the exact same thing I inputted



Integrate[Abs[f[x] - g[x]], x]


How do I fix this?






calculus-and-analysis







share|improve this question









New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I'm trying to solve and approximate the area between the two graphs. Right now, my functions are stored as



f[x_] := 3 Sin[x]
g[x_] := x - 1


and then I tried to integrate by evaluating



Integrate[Abs[f[x] - g[x]], x]


Instead of getting an answer, I just get the exact same thing I inputted



Integrate[Abs[f[x] - g[x]], x]


How do I fix this?






calculus-and-analysis




calculus-and-analysis






share|improve this question









New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 53 mins ago









m_goldberg

88.6k873200




88.6k873200






New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 1 hour ago









RyanRyan

111




111




New contributor




Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Ryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











  • $begingroup$
    You can format inline code and code blocks by selecting the code and clicking the button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful
    $endgroup$
    – Michael E2
    1 hour ago
















  • $begingroup$
    You can format inline code and code blocks by selecting the code and clicking the button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful
    $endgroup$
    – Michael E2
    1 hour ago















$begingroup$
You can format inline code and code blocks by selecting the code and clicking the button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful
$endgroup$
– Michael E2
1 hour ago




$begingroup$
You can format inline code and code blocks by selecting the code and clicking the button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful
$endgroup$
– Michael E2
1 hour ago










3 Answers
3






active

oldest

votes


















2












$begingroup$

Use Assumptions:



Integrate[Abs[f[x] - g[x]], x, Assumptions -> x [Element] Reals]


Mathematica graphics



Or try RealAbs instead of Abs:



Integrate[RealAbs[f[x] - g[x]], x]


Mathematica graphics



(They are equivalent antiderivatives.)



To get the area between the graphs, you need also to solve for the points of intersection.



area = Integrate[
 Abs[f[x] - g[x]], x, Sequence @@ MinMax[x /. Solve[f[x] == g[x], x, Reals]]]


Mathematica graphics



The area is approximately:



N[area]
(* 5.57475 *)





share|improve this answer











$endgroup$












  • $begingroup$
    RealAbs is awesome to know about! :O
    $endgroup$
    – Kagaratsch
    1 hour ago


















1












$begingroup$

You need to add assumptions, like this



 Integrate[Abs[f[x] - g[x]], x, Assumptions :> Element[x, Reals]]


Mathematica graphics






share|improve this answer









$endgroup$




















    0












    $begingroup$

    Assuming your functions



    f[x_] := 3 Sin[x] 
    g[x_] := x - 1


    are real valued, you can use square root of square to parametrize the absolute value. This then gives:



    Integrate[Sqrt[(f[x] - g[x])^2], x]



    (((-2 + x) x + 6 Cos[x]) Sqrt[(-1 + x - 3 Sin[x])^2])/(2 (-1 + x -
    3 Sin[x]))







    share|improve this answer









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function ()
      return StackExchange.using("mathjaxEditing", function ()
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      );
      );
      , "mathjax-editing");

      StackExchange.ready(function()
      var channelOptions =
      tags: "".split(" "),
      id: "387"
      ;
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function()
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled)
      StackExchange.using("snippets", function()
      createEditor();
      );

      else
      createEditor();

      );

      function createEditor()
      StackExchange.prepareEditor(
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: false,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: null,
      bindNavPrevention: true,
      postfix: "",
      imageUploader:
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      ,
      onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      );



      );






      Ryan is a new contributor. Be nice, and check out our Code of Conduct.









      draft saved

      draft discarded


















      StackExchange.ready(
      function ()
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f195049%2ffinding-the-area-between-two-curves-with-integrate%23new-answer', 'question_page');

      );

      Post as a guest















      Required, but never shown

























      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2












      $begingroup$

      Use Assumptions:



      Integrate[Abs[f[x] - g[x]], x, Assumptions -> x [Element] Reals]


      Mathematica graphics



      Or try RealAbs instead of Abs:



      Integrate[RealAbs[f[x] - g[x]], x]


      Mathematica graphics



      (They are equivalent antiderivatives.)



      To get the area between the graphs, you need also to solve for the points of intersection.



      area = Integrate[
       Abs[f[x] - g[x]], x, Sequence @@ MinMax[x /. Solve[f[x] == g[x], x, Reals]]]


      Mathematica graphics



      The area is approximately:



      N[area]
      (* 5.57475 *)





      share|improve this answer











      $endgroup$












      • $begingroup$
        RealAbs is awesome to know about! :O
        $endgroup$
        – Kagaratsch
        1 hour ago















      2












      $begingroup$

      Use Assumptions:



      Integrate[Abs[f[x] - g[x]], x, Assumptions -> x [Element] Reals]


      Mathematica graphics



      Or try RealAbs instead of Abs:



      Integrate[RealAbs[f[x] - g[x]], x]


      Mathematica graphics



      (They are equivalent antiderivatives.)



      To get the area between the graphs, you need also to solve for the points of intersection.



      area = Integrate[
       Abs[f[x] - g[x]], x, Sequence @@ MinMax[x /. Solve[f[x] == g[x], x, Reals]]]


      Mathematica graphics



      The area is approximately:



      N[area]
      (* 5.57475 *)





      share|improve this answer











      $endgroup$












      • $begingroup$
        RealAbs is awesome to know about! :O
        $endgroup$
        – Kagaratsch
        1 hour ago













      2












      2








      2





      $begingroup$

      Use Assumptions:



      Integrate[Abs[f[x] - g[x]], x, Assumptions -> x [Element] Reals]


      Mathematica graphics



      Or try RealAbs instead of Abs:



      Integrate[RealAbs[f[x] - g[x]], x]


      Mathematica graphics



      (They are equivalent antiderivatives.)



      To get the area between the graphs, you need also to solve for the points of intersection.



      area = Integrate[
       Abs[f[x] - g[x]], x, Sequence @@ MinMax[x /. Solve[f[x] == g[x], x, Reals]]]


      Mathematica graphics



      The area is approximately:



      N[area]
      (* 5.57475 *)





      share|improve this answer











      $endgroup$



      Use Assumptions:



      Integrate[Abs[f[x] - g[x]], x, Assumptions -> x [Element] Reals]


      Mathematica graphics



      Or try RealAbs instead of Abs:



      Integrate[RealAbs[f[x] - g[x]], x]


      Mathematica graphics



      (They are equivalent antiderivatives.)



      To get the area between the graphs, you need also to solve for the points of intersection.



      area = Integrate[
       Abs[f[x] - g[x]], x, Sequence @@ MinMax[x /. Solve[f[x] == g[x], x, Reals]]]


      Mathematica graphics



      The area is approximately:



      N[area]
      (* 5.57475 *)






      share|improve this answer














      share|improve this answer



      share|improve this answer








      edited 1 hour ago

























      answered 1 hour ago









      Michael E2Michael E2

      150k12203482




      150k12203482











      • $begingroup$
        RealAbs is awesome to know about! :O
        $endgroup$
        – Kagaratsch
        1 hour ago
















      • $begingroup$
        RealAbs is awesome to know about! :O
        $endgroup$
        – Kagaratsch
        1 hour ago















      $begingroup$
      RealAbs is awesome to know about! :O
      $endgroup$
      – Kagaratsch
      1 hour ago




      $begingroup$
      RealAbs is awesome to know about! :O
      $endgroup$
      – Kagaratsch
      1 hour ago











      1












      $begingroup$

      You need to add assumptions, like this



       Integrate[Abs[f[x] - g[x]], x, Assumptions :> Element[x, Reals]]


      Mathematica graphics






      share|improve this answer









      $endgroup$

















        1












        $begingroup$

        You need to add assumptions, like this



         Integrate[Abs[f[x] - g[x]], x, Assumptions :> Element[x, Reals]]


        Mathematica graphics






        share|improve this answer









        $endgroup$















          1












          1








          1





          $begingroup$

          You need to add assumptions, like this



           Integrate[Abs[f[x] - g[x]], x, Assumptions :> Element[x, Reals]]


          Mathematica graphics






          share|improve this answer









          $endgroup$



          You need to add assumptions, like this



           Integrate[Abs[f[x] - g[x]], x, Assumptions :> Element[x, Reals]]


          Mathematica graphics







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 1 hour ago









          NasserNasser

          58.7k490206




          58.7k490206





















              0












              $begingroup$

              Assuming your functions



              f[x_] := 3 Sin[x] 
              g[x_] := x - 1


              are real valued, you can use square root of square to parametrize the absolute value. This then gives:



              Integrate[Sqrt[(f[x] - g[x])^2], x]



              (((-2 + x) x + 6 Cos[x]) Sqrt[(-1 + x - 3 Sin[x])^2])/(2 (-1 + x -
              3 Sin[x]))







              share|improve this answer









              $endgroup$

















                0












                $begingroup$

                Assuming your functions



                f[x_] := 3 Sin[x] 
                g[x_] := x - 1


                are real valued, you can use square root of square to parametrize the absolute value. This then gives:



                Integrate[Sqrt[(f[x] - g[x])^2], x]



                (((-2 + x) x + 6 Cos[x]) Sqrt[(-1 + x - 3 Sin[x])^2])/(2 (-1 + x -
                3 Sin[x]))







                share|improve this answer









                $endgroup$















                  0












                  0








                  0





                  $begingroup$

                  Assuming your functions



                  f[x_] := 3 Sin[x] 
                  g[x_] := x - 1


                  are real valued, you can use square root of square to parametrize the absolute value. This then gives:



                  Integrate[Sqrt[(f[x] - g[x])^2], x]



                  (((-2 + x) x + 6 Cos[x]) Sqrt[(-1 + x - 3 Sin[x])^2])/(2 (-1 + x -
                  3 Sin[x]))







                  share|improve this answer









                  $endgroup$



                  Assuming your functions



                  f[x_] := 3 Sin[x] 
                  g[x_] := x - 1


                  are real valued, you can use square root of square to parametrize the absolute value. This then gives:



                  Integrate[Sqrt[(f[x] - g[x])^2], x]



                  (((-2 + x) x + 6 Cos[x]) Sqrt[(-1 + x - 3 Sin[x])^2])/(2 (-1 + x -
                  3 Sin[x]))








                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 1 hour ago









                  KagaratschKagaratsch

                  4,83831348




                  4,83831348




















                      Ryan is a new contributor. Be nice, and check out our Code of Conduct.









                      draft saved

                      draft discarded


















                      Ryan is a new contributor. Be nice, and check out our Code of Conduct.












                      Ryan is a new contributor. Be nice, and check out our Code of Conduct.











                      Ryan is a new contributor. Be nice, and check out our Code of Conduct.














                      Thanks for contributing an answer to Mathematica Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …


                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.

                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function ()
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f195049%2ffinding-the-area-between-two-curves-with-integrate%23new-answer', 'question_page');

                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Log på Navigationsmenu

                      Image
                      DeutschEnglishEsperantofrançaisespañolitalianoNederlands (function()var node=document.getElementById("mw-dismissablenotice-anonplace");if(node)node.outerHTML="u003Cdiv class="mw-dismissable-notice"u003Eu003Cdiv class="mw-dismissable-notice-close"u003E[u003Ca tabindex="0" role="button"u003ELuku003C/au003E]u003C/divu003Eu003Cdiv class="mw-dismissable-notice-body"u003Eu003Cdiv id="localNotice" lang="da" dir="ltr"u003Eu003Cpu003EI u003Ca href="/wiki/Wikipedia:Fokusm%C3%A5ned/maj_2019" title="Wikipedia:Fokusmåned/maj 2019"u003Emaj 2019u003C/au003E fokuserer vi på u003Cbu003Elokaliteter i Danmark som ikke er beskrevet på dansk Wikipediau003C/bu003E.u003Cbr /u003EDu kan desuden deltage i årets u003Ciu003Eu003Ca href="/wiki/Bruger:Ramloser/for%C3%A5rskonkurrence_2019" title="Bruger:Ramloser/forårskonkurrence 2019"u003Eforårskonkurrenceu003C/au003Eu003C/iu...
                      Read more

                      Creating second map without labels using QGIS?How to lock map labels for inset map in Print Composer?How to Force the Showing of Labels of a Vector File in QGISQGIS Valmiera, Labels only show for part of polygonsRemoving duplicate point labels in QGISLabeling every feature using QGIS?Show labels for point features outside map canvasAbbreviate Road Labels in QGIS only when requiredExporting map from composer in QGIS - text labels have moved in output?How to make sure labels in qgis turn up in layout map?Writing label expression with ArcMap and If then Statement?

                      Image
                      Why is the Eisenstein ideal paper so great? What would prevent living skin from being a good conductor for magic? Using too much dialogue? Fixie: how to learn to ride: step by step Who knighted this character? The Maltese Falcon Expected maximum number of unpaired socks If I arrive in the UK, and then head to mainland Europe, does my Schengen visa 90 day limit start when I arrived in the UK, or mainland Europe? Why does Bran want to find Drogon? Why isn't Tyrion mentioned in 'A song of Ice and Fire'? Did this character show any indication of wanting to rule before S8E6? Should I split timestamp parts into separate columns? What were the Ethiopians doing in Xerxes' army? “For nothing” = “pour rien”? Can you still travel to America on the ESTA waiver program if you have been to Iran in transit? Can a UK national work as a paid shop assistant in the USA? Why does the Starter Set wizard have six spells in their spellbook? Why does sp...
                      Read more

                      Nuuk Indholdsfortegnelse Etyomologi | Historie | Geografi | Transport og infrastruktur | Politik og administration | Uddannelsesinstitutioner | Kultur | Venskabsbyer | Noter | Eksterne henvisninger | Se også | Navigationsmenuwww.sermersooq.gl64°10′N 51°45′V / 64.167°N 51.750°V / 64.167; -51.75064°10′N 51°45′V / 64.167°N 51.750°V / 64.167; -51.750DMI - KlimanormalerSalmonsen, s. 850Grønlands Naturinstitut undersøger rensdyr i Akia og Maniitsoq foråret 2008Grønlands NaturinstitutNy vej til Qinngorput indviet i dagAntallet af biler i Nuuk må begrænsesNy taxacentral mødt med demonstrationKøreplan. Rute 1, 2 og 3SnescootersporNuukNord er for storSkoler i Kommuneqarfik SermersooqAtuarfik Samuel KleinschmidtKangillinguit AtuarfiatNuussuup AtuarfiaNuuk Internationale FriskoleIlinniarfissuaq, Grønlands SeminariumLedelseÅrsberetning for 2008Kunst og arkitekturÅrsberetning for 2008Julie om naturenNuuk KunstmuseumSilamiutGrønlands Nationalmuseum og ArkivStatistisk ÅrbogGrønlands LandsbibliotekStore koncerter på stribeVandhund nummer 1.000.000Kommuneqarfik Sermersooq – MalikForsidenVenskabsbyerLyngby-Taarbæk i GrønlandArctic Business NetworkWinter Cities 2008 i NuukDagligt opdaterede satellitbilleder fra NuukområdetKommuneqarfik Sermersooqs hjemmesideTurist i NuukGrønlands Statistiks databankGrønlands Hjemmestyres valgresultaterrrWorldCat124325457671310-5

                      Image
                      CentrumNuussuaqKolonihavnenQernertunnguitQinngorputQuassussuup TungaaMyggedalenRadiofjeldetKatuaqNuuk CenterGrønlands Nationalmuseum og ArkivHotel Hans EgedeBrættetHerrnhuthusetNuuk KunstmuseumVor Frelser KirkeHans Egede KirkeNuuk TuristkontorSømandshjemmetHans Egedes statueArctic Umiaq LineNuuk LufthavnNuuk HavnNuup BussiiTaxagutNuuk TaxiRoyal Arctic LineRoyal GreenlandIlulissat (Jakobshavn)Qaanaaq (Thule)UpernavikUummannaqAappilattoqIkerasak (Sundet)Ilimanaq (Claushavn)IllorsuitInnaarsuitKangersuatsiaq (Prøven)Kullorsuaq (Djævelens Tommelfinger)MoriusaqNaajaatNiaqornatNutaarmiutNuugaatsiaqNuussuaq (Kraulshavn)Oqaatsut (Rodebay)QaarsutQeqertaqQeqertatSaattutSaqqaqSavissivikSiorapalukTasiusaqTussaaqUkkusissatUpernavik Kujalleq (Søndre Upernavik)Maniitsoq (Sukkertoppen)Sisimiut (Holsteinsborg)AtammikItilleqKangaamiut (Gammel Sukkertoppen)Kangerlussuaq (Søndre Strømfjord)NapasoqSarfannguitNanortalikNarsaqQaqortoq (Julianehåb)AappilattoqAlluitsu...
                      Read more