Can anyone help in $int_0^pi (sin x )^{cos x} dx$? [closed]












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I am trying to solve the following definite integral;




$int_0^pi (sin x )^{cos x} dx$?







definite-integrals







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closed as off-topic by Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost Dec 30 '18 at 14:19


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost

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  • $begingroup$
    @OmG Your input is wrong. You computed the integral of the function $xcdot sin(x)^{cos(x)}$ instead of $sin(x)^{cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand.
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    – mrtaurho
    Dec 8 '18 at 13:51


















3












$begingroup$


I am trying to solve the following definite integral;




$int_0^pi (sin x )^{cos x} dx$?







definite-integrals







share|cite|improve this question











$endgroup$



closed as off-topic by Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost Dec 30 '18 at 14:19


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.
















  • $begingroup$
    @OmG Your input is wrong. You computed the integral of the function $xcdot sin(x)^{cos(x)}$ instead of $sin(x)^{cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand.
    $endgroup$
    – mrtaurho
    Dec 8 '18 at 13:51
















3












3








3


1



$begingroup$


I am trying to solve the following definite integral;




$int_0^pi (sin x )^{cos x} dx$?







definite-integrals







share|cite|improve this question











$endgroup$




I am trying to solve the following definite integral;




$int_0^pi (sin x )^{cos x} dx$?







definite-integrals




definite-integrals






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 8 '18 at 14:07









amWhy

1




1










asked Dec 8 '18 at 13:25









AlbertAlbert

344




344




closed as off-topic by Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost Dec 30 '18 at 14:19


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost Dec 30 '18 at 14:19


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, mrtaurho, metamorphy, Martín Vacas Vignolo, Paul Frost

If this question can be reworded to fit the rules in the help center, please edit the question.












  • $begingroup$
    @OmG Your input is wrong. You computed the integral of the function $xcdot sin(x)^{cos(x)}$ instead of $sin(x)^{cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand.
    $endgroup$
    – mrtaurho
    Dec 8 '18 at 13:51




















  • $begingroup$
    @OmG Your input is wrong. You computed the integral of the function $xcdot sin(x)^{cos(x)}$ instead of $sin(x)^{cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand.
    $endgroup$
    – mrtaurho
    Dec 8 '18 at 13:51


















$begingroup$
@OmG Your input is wrong. You computed the integral of the function $xcdot sin(x)^{cos(x)}$ instead of $sin(x)^{cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand.
$endgroup$
– mrtaurho
Dec 8 '18 at 13:51






$begingroup$
@OmG Your input is wrong. You computed the integral of the function $xcdot sin(x)^{cos(x)}$ instead of $sin(x)^{cos(x)}$. It does not alter the fact that it does not converge but I would say it is important to be precise concerning the integrand.
$endgroup$
– mrtaurho
Dec 8 '18 at 13:51












1 Answer
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The integral does not exist, because $sin(pi-epsilon) = epsilon + o(epsilon^3)$ and $cos(pi-epsilon) = -1 + epsilon^2/2 + o(epsilon^3),$ i.e. the integrand has a pole at $x=pi.$






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

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    active

    oldest

    votes









    3












    $begingroup$

    The integral does not exist, because $sin(pi-epsilon) = epsilon + o(epsilon^3)$ and $cos(pi-epsilon) = -1 + epsilon^2/2 + o(epsilon^3),$ i.e. the integrand has a pole at $x=pi.$






    share|cite|improve this answer











    $endgroup$


















      3












      $begingroup$

      The integral does not exist, because $sin(pi-epsilon) = epsilon + o(epsilon^3)$ and $cos(pi-epsilon) = -1 + epsilon^2/2 + o(epsilon^3),$ i.e. the integrand has a pole at $x=pi.$






      share|cite|improve this answer











      $endgroup$
















        3












        3








        3





        $begingroup$

        The integral does not exist, because $sin(pi-epsilon) = epsilon + o(epsilon^3)$ and $cos(pi-epsilon) = -1 + epsilon^2/2 + o(epsilon^3),$ i.e. the integrand has a pole at $x=pi.$






        share|cite|improve this answer











        $endgroup$



        The integral does not exist, because $sin(pi-epsilon) = epsilon + o(epsilon^3)$ and $cos(pi-epsilon) = -1 + epsilon^2/2 + o(epsilon^3),$ i.e. the integrand has a pole at $x=pi.$







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Dec 8 '18 at 13:59

























        answered Dec 8 '18 at 13:50









        gammatestergammatester

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        16.7k21633















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