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

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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
    2 hours 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
    2 hours 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 2 hours 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 2 hours 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
    2 hours 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
    2 hours 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
2 hours 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
2 hours 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
    2 hours 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





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      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
        2 hours 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
        2 hours 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 2 hours ago

























      answered 2 hours ago









      Michael E2Michael E2

      150k12203482




      150k12203482











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
















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















      $begingroup$
      RealAbs is awesome to know about! :O
      $endgroup$
      – Kagaratsch
      2 hours ago




      $begingroup$
      RealAbs is awesome to know about! :O
      $endgroup$
      – Kagaratsch
      2 hours 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 2 hours 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 2 hours ago









                  KagaratschKagaratsch

                  4,83831348




                  4,83831348




















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









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











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