Proof of an integral property [closed]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP












4












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$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$






calculus integration definite-integrals







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closed as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen Feb 22 at 0:58


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." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.











  • 8




    $begingroup$
    Do you know integration by parts?
    $endgroup$
    – Minus One-Twelfth
    Feb 21 at 1:37
















4












$begingroup$


$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$






calculus integration definite-integrals







share|cite|improve this question











$endgroup$



closed as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen Feb 22 at 0:58


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." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.











  • 8




    $begingroup$
    Do you know integration by parts?
    $endgroup$
    – Minus One-Twelfth
    Feb 21 at 1:37














4












4








4





$begingroup$


$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$






calculus integration definite-integrals







share|cite|improve this question











$endgroup$




$$int_0^1 f(x)g'(x)dx=pi$$ If $f(1)g(1)=f(0)g(0)$ then $$int_0^1 f'(x)g(x)dx= -pi$$
So I have to prove this and I have absolutely no idea how to do it. I am guessing I will have to use the fundamental theorem of calculus and it show that the rate of change is $1$ because it didn't change from $f(1)g(1)$ to $f(0)g(0)$






calculus integration definite-integrals




calculus integration definite-integrals






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share|cite|improve this question













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edited Feb 21 at 1:41









Eevee Trainer

7,96821439




7,96821439










asked Feb 21 at 1:36









adam hanyadam hany

212




212




closed as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen Feb 22 at 0:58


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." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by RRL, stressed out, Song, Cesareo, Kemono Chen Feb 22 at 0:58


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." – RRL, stressed out, Song, Cesareo, Kemono Chen
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 8




    $begingroup$
    Do you know integration by parts?
    $endgroup$
    – Minus One-Twelfth
    Feb 21 at 1:37













  • 8




    $begingroup$
    Do you know integration by parts?
    $endgroup$
    – Minus One-Twelfth
    Feb 21 at 1:37








8




8




$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
Feb 21 at 1:37





$begingroup$
Do you know integration by parts?
$endgroup$
– Minus One-Twelfth
Feb 21 at 1:37











2 Answers
2






active

oldest

votes


















5












$begingroup$

Hint:



Utilize integration by parts:



$$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$



If we have a definite integral, then this formula becomes



$$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$






share|cite|improve this answer











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  • 1




    $begingroup$
    thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
    $endgroup$
    – adam hany
    Feb 21 at 2:01


















3












$begingroup$

Hint:



$$dfracd(f(x)cdot g(x))dx=?$$



Integrate both sides with respect to $x$ between $[0,1]$






share|cite|improve this answer











$endgroup$



















    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    5












    $begingroup$

    Hint:



    Utilize integration by parts:



    $$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$



    If we have a definite integral, then this formula becomes



    $$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$






    share|cite|improve this answer











    $endgroup$








    • 1




      $begingroup$
      thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
      $endgroup$
      – adam hany
      Feb 21 at 2:01















    5












    $begingroup$

    Hint:



    Utilize integration by parts:



    $$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$



    If we have a definite integral, then this formula becomes



    $$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$






    share|cite|improve this answer











    $endgroup$








    • 1




      $begingroup$
      thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
      $endgroup$
      – adam hany
      Feb 21 at 2:01













    5












    5








    5





    $begingroup$

    Hint:



    Utilize integration by parts:



    $$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$



    If we have a definite integral, then this formula becomes



    $$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$






    share|cite|improve this answer











    $endgroup$



    Hint:



    Utilize integration by parts:



    $$int f(x)g'(x)mathrm dx = f(x)g(x) - int f'(x)g(x) mathrm dx$$



    If we have a definite integral, then this formula becomes



    $$int_a^b f(x)g'(x)mathrm dx = f(b)g(b) - f(a)g(a) - int_a^b f'(x)g(x) mathrm dx$$







    share|cite|improve this answer














    share|cite|improve this answer



    share|cite|improve this answer








    edited Feb 21 at 6:42









    mrtaurho

    6,00551641




    6,00551641










    answered Feb 21 at 1:39









    Eevee TrainerEevee Trainer

    7,96821439




    7,96821439







    • 1




      $begingroup$
      thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
      $endgroup$
      – adam hany
      Feb 21 at 2:01












    • 1




      $begingroup$
      thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
      $endgroup$
      – adam hany
      Feb 21 at 2:01







    1




    1




    $begingroup$
    thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
    $endgroup$
    – adam hany
    Feb 21 at 2:01




    $begingroup$
    thank you so much for the answer ∫baf(x)g′(x)dx=−∫baf′(x)g(x)
    $endgroup$
    – adam hany
    Feb 21 at 2:01











    3












    $begingroup$

    Hint:



    $$dfracd(f(x)cdot g(x))dx=?$$



    Integrate both sides with respect to $x$ between $[0,1]$






    share|cite|improve this answer











    $endgroup$

















      3












      $begingroup$

      Hint:



      $$dfracd(f(x)cdot g(x))dx=?$$



      Integrate both sides with respect to $x$ between $[0,1]$






      share|cite|improve this answer











      $endgroup$















        3












        3








        3





        $begingroup$

        Hint:



        $$dfracd(f(x)cdot g(x))dx=?$$



        Integrate both sides with respect to $x$ between $[0,1]$






        share|cite|improve this answer











        $endgroup$



        Hint:



        $$dfracd(f(x)cdot g(x))dx=?$$



        Integrate both sides with respect to $x$ between $[0,1]$







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Feb 21 at 6:09









        Eevee Trainer

        7,96821439




        7,96821439










        answered Feb 21 at 2:05









        lab bhattacharjeelab bhattacharjee

        227k15158275




        227k15158275












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