Integration Help Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm...

Is safe to use va_start macro with this as parameter?

What are the out-of-universe reasons for the references to Toby Maguire-era Spider-Man in ITSV

How do I find out the mythology and history of my Fortress?

Circuit to "zoom in" on mV fluctuations of a DC signal?

Can an alien society believe that their star system is the universe?

What does "lightly crushed" mean for cardamon pods?

Generate an RGB colour grid

Did MS DOS itself ever use blinking text?

Would "destroying" Wurmcoil Engine prevent its tokens from being created?

How can I use the Python library networkx from Mathematica?

How to find all the available tools in mac terminal?

Does classifying an integer as a discrete log require it be part of a multiplicative group?

How to show element name in portuguese using elements package?

Extracting terms with certain heads in a function

What is the meaning of the simile “quick as silk”?

What is homebrew?

Can a party unilaterally change candidates in preparation for a General election?

First console to have temporary backward compatibility

How do pianists reach extremely loud dynamics?

2001: A Space Odyssey's use of the song "Daisy Bell" (Bicycle Built for Two); life imitates art or vice-versa?

Where are Serre’s lectures at Collège de France to be found?

Using et al. for a last / senior author rather than for a first author

Dating a Former Employee

Integration Help



Integration Help



Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?Understanding output of multivariable integrationHow do I generate arbitrarily many integration bounds?Getting long complex-valued integrals when simpler real-valued expressions existsymbolic integration of product of hankel function and trignometric functionA Chain rule proof using MathematicaHelp with IntegrationHow to solve this integration?How to get the partial derivative of the inverse functions?Possible bug in integration involving $cos (n phi)$Integration with parameter












1












$begingroup$


So I have to integrate $$frac{sin^n x}{sin^n x + cos^n x}$$ and am coding this in Mathematica with



 (((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x]))) 


with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.



I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is



 (((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))), 


but does not solve it. Anyone know how to help or fix this??










share|improve this question









New contributor




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







$endgroup$








  • 1




    $begingroup$
    Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using (Sin^2)[x] when that syntax is incorrect, you should instead write it as Sin[x]^2
    $endgroup$
    – enano9314
    4 hours ago












  • $begingroup$
    Related: math.stackexchange.com/questions/82489/…
    $endgroup$
    – Michael E2
    50 mins ago
















1












$begingroup$


So I have to integrate $$frac{sin^n x}{sin^n x + cos^n x}$$ and am coding this in Mathematica with



 (((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x]))) 


with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.



I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is



 (((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))), 


but does not solve it. Anyone know how to help or fix this??










share|improve this question









New contributor




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







$endgroup$








  • 1




    $begingroup$
    Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using (Sin^2)[x] when that syntax is incorrect, you should instead write it as Sin[x]^2
    $endgroup$
    – enano9314
    4 hours ago












  • $begingroup$
    Related: math.stackexchange.com/questions/82489/…
    $endgroup$
    – Michael E2
    50 mins ago














1












1








1





$begingroup$


So I have to integrate $$frac{sin^n x}{sin^n x + cos^n x}$$ and am coding this in Mathematica with



 (((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x]))) 


with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.



I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is



 (((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))), 


but does not solve it. Anyone know how to help or fix this??










share|improve this question









New contributor




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







$endgroup$




So I have to integrate $$frac{sin^n x}{sin^n x + cos^n x}$$ and am coding this in Mathematica with



 (((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x]))) 


with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.



I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is



 (((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))), 


but does not solve it. Anyone know how to help or fix this??







calculus-and-analysis






share|improve this question









New contributor




Emma 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




Emma 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 1 hour ago









Michael E2

151k12203482




151k12203482






New contributor




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









asked 4 hours ago









EmmaEmma

61




61




New contributor




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





New contributor





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






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








  • 1




    $begingroup$
    Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using (Sin^2)[x] when that syntax is incorrect, you should instead write it as Sin[x]^2
    $endgroup$
    – enano9314
    4 hours ago












  • $begingroup$
    Related: math.stackexchange.com/questions/82489/…
    $endgroup$
    – Michael E2
    50 mins ago














  • 1




    $begingroup$
    Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using (Sin^2)[x] when that syntax is incorrect, you should instead write it as Sin[x]^2
    $endgroup$
    – enano9314
    4 hours ago












  • $begingroup$
    Related: math.stackexchange.com/questions/82489/…
    $endgroup$
    – Michael E2
    50 mins ago








1




1




$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using (Sin^2)[x] when that syntax is incorrect, you should instead write it as Sin[x]^2
$endgroup$
– enano9314
4 hours ago






$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using (Sin^2)[x] when that syntax is incorrect, you should instead write it as Sin[x]^2
$endgroup$
– enano9314
4 hours ago














$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
50 mins ago




$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
50 mins ago










3 Answers
3






active

oldest

votes


















3












$begingroup$

This works for me:



Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),{x,0,Pi/2}],{n,1,5}]


And it gives the output {Pi/4,Pi/4,Pi/4,Pi/4,Pi/4}.



enter image description here






share|improve this answer











$endgroup$









  • 1




    $begingroup$
    Recommend that you add a Plot to make it easier to understand why the result is a constant.
    $endgroup$
    – Bob Hanlon
    3 hours ago










  • $begingroup$
    Good suggestion. Editing.
    $endgroup$
    – Kevin Ausman
    3 hours ago



















2












$begingroup$

Perhaps you're writing your function in the wrong format Emma. The following works fine:



n = 2;
Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),{x, 0, π/2}]



π/4







share|improve this answer











$endgroup$













  • $begingroup$
    I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
    $endgroup$
    – Kevin Ausman
    4 hours ago






  • 1




    $begingroup$
    Yes, just realized that, thanks for pointing it out.
    $endgroup$
    – amator2357
    3 hours ago



















1












$begingroup$

A common trick (see this Math.SE post:



ClearAll[symmetrizeIntegrate];
SetAttributes[symmetrizeIntegrate, HoldAll];
symmetrizeIntegrate[Integrate[f_, {x_, a_, b_}, opts___]] :=
Integrate[(f + (f /. x -> a + b - x))/2, {x, a, b}, opts]

symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, [Pi]/2}]]
(* [Pi]/4 *)





share|improve this answer









$endgroup$














    Your Answer








    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
    });


    }
    });






    Emma 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%2f195438%2fintegration-help%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









    3












    $begingroup$

    This works for me:



    Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),{x,0,Pi/2}],{n,1,5}]


    And it gives the output {Pi/4,Pi/4,Pi/4,Pi/4,Pi/4}.



    enter image description here






    share|improve this answer











    $endgroup$









    • 1




      $begingroup$
      Recommend that you add a Plot to make it easier to understand why the result is a constant.
      $endgroup$
      – Bob Hanlon
      3 hours ago










    • $begingroup$
      Good suggestion. Editing.
      $endgroup$
      – Kevin Ausman
      3 hours ago
















    3












    $begingroup$

    This works for me:



    Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),{x,0,Pi/2}],{n,1,5}]


    And it gives the output {Pi/4,Pi/4,Pi/4,Pi/4,Pi/4}.



    enter image description here






    share|improve this answer











    $endgroup$









    • 1




      $begingroup$
      Recommend that you add a Plot to make it easier to understand why the result is a constant.
      $endgroup$
      – Bob Hanlon
      3 hours ago










    • $begingroup$
      Good suggestion. Editing.
      $endgroup$
      – Kevin Ausman
      3 hours ago














    3












    3








    3





    $begingroup$

    This works for me:



    Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),{x,0,Pi/2}],{n,1,5}]


    And it gives the output {Pi/4,Pi/4,Pi/4,Pi/4,Pi/4}.



    enter image description here






    share|improve this answer











    $endgroup$



    This works for me:



    Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),{x,0,Pi/2}],{n,1,5}]


    And it gives the output {Pi/4,Pi/4,Pi/4,Pi/4,Pi/4}.



    enter image description here







    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 3 hours ago

























    answered 4 hours ago









    Kevin AusmanKevin Ausman

    32417




    32417








    • 1




      $begingroup$
      Recommend that you add a Plot to make it easier to understand why the result is a constant.
      $endgroup$
      – Bob Hanlon
      3 hours ago










    • $begingroup$
      Good suggestion. Editing.
      $endgroup$
      – Kevin Ausman
      3 hours ago














    • 1




      $begingroup$
      Recommend that you add a Plot to make it easier to understand why the result is a constant.
      $endgroup$
      – Bob Hanlon
      3 hours ago










    • $begingroup$
      Good suggestion. Editing.
      $endgroup$
      – Kevin Ausman
      3 hours ago








    1




    1




    $begingroup$
    Recommend that you add a Plot to make it easier to understand why the result is a constant.
    $endgroup$
    – Bob Hanlon
    3 hours ago




    $begingroup$
    Recommend that you add a Plot to make it easier to understand why the result is a constant.
    $endgroup$
    – Bob Hanlon
    3 hours ago












    $begingroup$
    Good suggestion. Editing.
    $endgroup$
    – Kevin Ausman
    3 hours ago




    $begingroup$
    Good suggestion. Editing.
    $endgroup$
    – Kevin Ausman
    3 hours ago











    2












    $begingroup$

    Perhaps you're writing your function in the wrong format Emma. The following works fine:



    n = 2;
    Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),{x, 0, π/2}]



    π/4







    share|improve this answer











    $endgroup$













    • $begingroup$
      I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
      $endgroup$
      – Kevin Ausman
      4 hours ago






    • 1




      $begingroup$
      Yes, just realized that, thanks for pointing it out.
      $endgroup$
      – amator2357
      3 hours ago
















    2












    $begingroup$

    Perhaps you're writing your function in the wrong format Emma. The following works fine:



    n = 2;
    Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),{x, 0, π/2}]



    π/4







    share|improve this answer











    $endgroup$













    • $begingroup$
      I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
      $endgroup$
      – Kevin Ausman
      4 hours ago






    • 1




      $begingroup$
      Yes, just realized that, thanks for pointing it out.
      $endgroup$
      – amator2357
      3 hours ago














    2












    2








    2





    $begingroup$

    Perhaps you're writing your function in the wrong format Emma. The following works fine:



    n = 2;
    Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),{x, 0, π/2}]



    π/4







    share|improve this answer











    $endgroup$



    Perhaps you're writing your function in the wrong format Emma. The following works fine:



    n = 2;
    Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),{x, 0, π/2}]



    π/4








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 2 hours ago









    m_goldberg

    88.8k873200




    88.8k873200










    answered 4 hours ago









    amator2357amator2357

    1437




    1437












    • $begingroup$
      I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
      $endgroup$
      – Kevin Ausman
      4 hours ago






    • 1




      $begingroup$
      Yes, just realized that, thanks for pointing it out.
      $endgroup$
      – amator2357
      3 hours ago


















    • $begingroup$
      I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
      $endgroup$
      – Kevin Ausman
      4 hours ago






    • 1




      $begingroup$
      Yes, just realized that, thanks for pointing it out.
      $endgroup$
      – amator2357
      3 hours ago
















    $begingroup$
    I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
    $endgroup$
    – Kevin Ausman
    4 hours ago




    $begingroup$
    I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
    $endgroup$
    – Kevin Ausman
    4 hours ago




    1




    1




    $begingroup$
    Yes, just realized that, thanks for pointing it out.
    $endgroup$
    – amator2357
    3 hours ago




    $begingroup$
    Yes, just realized that, thanks for pointing it out.
    $endgroup$
    – amator2357
    3 hours ago











    1












    $begingroup$

    A common trick (see this Math.SE post:



    ClearAll[symmetrizeIntegrate];
    SetAttributes[symmetrizeIntegrate, HoldAll];
    symmetrizeIntegrate[Integrate[f_, {x_, a_, b_}, opts___]] :=
    Integrate[(f + (f /. x -> a + b - x))/2, {x, a, b}, opts]

    symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, [Pi]/2}]]
    (* [Pi]/4 *)





    share|improve this answer









    $endgroup$


















      1












      $begingroup$

      A common trick (see this Math.SE post:



      ClearAll[symmetrizeIntegrate];
      SetAttributes[symmetrizeIntegrate, HoldAll];
      symmetrizeIntegrate[Integrate[f_, {x_, a_, b_}, opts___]] :=
      Integrate[(f + (f /. x -> a + b - x))/2, {x, a, b}, opts]

      symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, [Pi]/2}]]
      (* [Pi]/4 *)





      share|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        A common trick (see this Math.SE post:



        ClearAll[symmetrizeIntegrate];
        SetAttributes[symmetrizeIntegrate, HoldAll];
        symmetrizeIntegrate[Integrate[f_, {x_, a_, b_}, opts___]] :=
        Integrate[(f + (f /. x -> a + b - x))/2, {x, a, b}, opts]

        symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, [Pi]/2}]]
        (* [Pi]/4 *)





        share|improve this answer









        $endgroup$



        A common trick (see this Math.SE post:



        ClearAll[symmetrizeIntegrate];
        SetAttributes[symmetrizeIntegrate, HoldAll];
        symmetrizeIntegrate[Integrate[f_, {x_, a_, b_}, opts___]] :=
        Integrate[(f + (f /. x -> a + b - x))/2, {x, a, b}, opts]

        symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, [Pi]/2}]]
        (* [Pi]/4 *)






        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 41 mins ago









        Michael E2Michael E2

        151k12203482




        151k12203482






















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










            draft saved

            draft discarded


















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













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












            Emma 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%2f195438%2fintegration-help%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

            El tren de la libertad Índice Antecedentes "Porque yo decido" Desarrollo de la...

            Puerta de Hutt Referencias Enlaces externos Menú de navegación15°58′00″S 5°42′00″O /...

            Castillo d'Acher Características Menú de navegación