How to obtain the logarithm from this numerical integral?

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Evaluate $int_0^1fracdx1+x$ using the trapezoidal rule for integration and hence find the value of $log(2)$.




I solved the first part with an interval of 0.125 and obtained: $int_0^1fracdx1+x ≈ 0.694075$. However, how do I find the value of $log(2)$ in this context?






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    Evaluate $int_0^1fracdx1+x$ using the trapezoidal rule for integration and hence find the value of $log(2)$.




    I solved the first part with an interval of 0.125 and obtained: $int_0^1fracdx1+x ≈ 0.694075$. However, how do I find the value of $log(2)$ in this context?






    numerical-methods







    share|cite|improve this question









    New contributor




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





















      up vote
      4
      down vote

      favorite









      up vote
      4
      down vote

      favorite












      Evaluate $int_0^1fracdx1+x$ using the trapezoidal rule for integration and hence find the value of $log(2)$.




      I solved the first part with an interval of 0.125 and obtained: $int_0^1fracdx1+x ≈ 0.694075$. However, how do I find the value of $log(2)$ in this context?






      numerical-methods







      share|cite|improve this question









      New contributor




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












      Evaluate $int_0^1fracdx1+x$ using the trapezoidal rule for integration and hence find the value of $log(2)$.




      I solved the first part with an interval of 0.125 and obtained: $int_0^1fracdx1+x ≈ 0.694075$. However, how do I find the value of $log(2)$ in this context?






      numerical-methods




      numerical-methods






      share|cite|improve this question









      New contributor




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











      share|cite|improve this question









      New contributor




      Dipendra Shrestha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      edited 20 mins ago









      Wrzlprmft

      2,86411233




      2,86411233






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      asked 3 hours ago









      Dipendra Shrestha

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          2 Answers
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          You have already found the value of $log(2)$. Congrats!



          Hint:



          $$int_0^1fracmathrmdx1+x=log(2)$$



          So there you have your context and what you have found is the value of the integration i.e. $log(2)$ by using numerical methods (Trapezoidal rule).






          share|cite|improve this answer





























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            $$int_a^b frac11+xdx=log_e(1+x)|_a^b=log_e(1+b) - log_e(1+a)=log_efrac1+b1+a$$



            For $a=0$ and $b=1$ this goes to $log_e2$






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              2 Answers
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              up vote
              4
              down vote













              You have already found the value of $log(2)$. Congrats!



              Hint:



              $$int_0^1fracmathrmdx1+x=log(2)$$



              So there you have your context and what you have found is the value of the integration i.e. $log(2)$ by using numerical methods (Trapezoidal rule).






              share|cite|improve this answer


























                up vote
                4
                down vote













                You have already found the value of $log(2)$. Congrats!



                Hint:



                $$int_0^1fracmathrmdx1+x=log(2)$$



                So there you have your context and what you have found is the value of the integration i.e. $log(2)$ by using numerical methods (Trapezoidal rule).






                share|cite|improve this answer
























                  up vote
                  4
                  down vote










                  up vote
                  4
                  down vote









                  You have already found the value of $log(2)$. Congrats!



                  Hint:



                  $$int_0^1fracmathrmdx1+x=log(2)$$



                  So there you have your context and what you have found is the value of the integration i.e. $log(2)$ by using numerical methods (Trapezoidal rule).






                  share|cite|improve this answer














                  You have already found the value of $log(2)$. Congrats!



                  Hint:



                  $$int_0^1fracmathrmdx1+x=log(2)$$



                  So there you have your context and what you have found is the value of the integration i.e. $log(2)$ by using numerical methods (Trapezoidal rule).







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited 2 hours ago

























                  answered 3 hours ago









                  paulplusx

                  942217




                  942217




















                      up vote
                      1
                      down vote













                      $$int_a^b frac11+xdx=log_e(1+x)|_a^b=log_e(1+b) - log_e(1+a)=log_efrac1+b1+a$$



                      For $a=0$ and $b=1$ this goes to $log_e2$






                      share|cite|improve this answer


























                        up vote
                        1
                        down vote













                        $$int_a^b frac11+xdx=log_e(1+x)|_a^b=log_e(1+b) - log_e(1+a)=log_efrac1+b1+a$$



                        For $a=0$ and $b=1$ this goes to $log_e2$






                        share|cite|improve this answer
























                          up vote
                          1
                          down vote










                          up vote
                          1
                          down vote









                          $$int_a^b frac11+xdx=log_e(1+x)|_a^b=log_e(1+b) - log_e(1+a)=log_efrac1+b1+a$$



                          For $a=0$ and $b=1$ this goes to $log_e2$






                          share|cite|improve this answer














                          $$int_a^b frac11+xdx=log_e(1+x)|_a^b=log_e(1+b) - log_e(1+a)=log_efrac1+b1+a$$



                          For $a=0$ and $b=1$ this goes to $log_e2$







                          share|cite|improve this answer














                          share|cite|improve this answer



                          share|cite|improve this answer








                          edited 8 mins ago









                          Glorfindel

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                          3,21371729










                          answered 2 hours ago









                          Derek

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                          989613




















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