indicator function with integrals

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I have a following integral



$$int_0^T-bfleft(tauright)dtau$$



where $T-b$ is an arbitrary constant number. I try to change the limits of this integral by using an indicator function and I write



$$int_0^nfleft(tauright)dtauboldsymbol1_tauleq T-b$$



where $n$ is an arbitrary value. I am not sure if it is a correct way to write the integral in this way. And also, I am trying to use the fundamental theorem of calculus as



$$fleft(nright)boldsymbol1_nleq T-b$$



Am I allowed to do these operations? If not, how can I correct my mistakes?




calculus integration definite-integrals upper-lower-bounds




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    up vote
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    down vote

    favorite












    I have a following integral



    $$int_0^T-bfleft(tauright)dtau$$



    where $T-b$ is an arbitrary constant number. I try to change the limits of this integral by using an indicator function and I write



    $$int_0^nfleft(tauright)dtauboldsymbol1_tauleq T-b$$



    where $n$ is an arbitrary value. I am not sure if it is a correct way to write the integral in this way. And also, I am trying to use the fundamental theorem of calculus as



    $$fleft(nright)boldsymbol1_nleq T-b$$



    Am I allowed to do these operations? If not, how can I correct my mistakes?




    calculus integration definite-integrals upper-lower-bounds




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I have a following integral



      $$int_0^T-bfleft(tauright)dtau$$



      where $T-b$ is an arbitrary constant number. I try to change the limits of this integral by using an indicator function and I write



      $$int_0^nfleft(tauright)dtauboldsymbol1_tauleq T-b$$



      where $n$ is an arbitrary value. I am not sure if it is a correct way to write the integral in this way. And also, I am trying to use the fundamental theorem of calculus as



      $$fleft(nright)boldsymbol1_nleq T-b$$



      Am I allowed to do these operations? If not, how can I correct my mistakes?




      calculus integration definite-integrals upper-lower-bounds




      share|cite|improve this question











      I have a following integral



      $$int_0^T-bfleft(tauright)dtau$$



      where $T-b$ is an arbitrary constant number. I try to change the limits of this integral by using an indicator function and I write



      $$int_0^nfleft(tauright)dtauboldsymbol1_tauleq T-b$$



      where $n$ is an arbitrary value. I am not sure if it is a correct way to write the integral in this way. And also, I am trying to use the fundamental theorem of calculus as



      $$fleft(nright)boldsymbol1_nleq T-b$$



      Am I allowed to do these operations? If not, how can I correct my mistakes?





      calculus integration definite-integrals upper-lower-bounds





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 28 at 8:35









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