Integration of greatest integer function [closed]












0












$begingroup$


Let $[x]$ denote the greatest integer function, then evaluate



$$int_{-100}^{100}[x^3]dx$$



I have no idea how to go about it, can someone help me out










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$endgroup$



closed as off-topic by RRL, Alexander Gruber Jan 17 at 23:21


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, Alexander Gruber

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





















    0












    $begingroup$


    Let $[x]$ denote the greatest integer function, then evaluate



    $$int_{-100}^{100}[x^3]dx$$



    I have no idea how to go about it, can someone help me out










    share|cite|improve this question









    $endgroup$



    closed as off-topic by RRL, Alexander Gruber Jan 17 at 23:21


    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, Alexander Gruber

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



















      0












      0








      0





      $begingroup$


      Let $[x]$ denote the greatest integer function, then evaluate



      $$int_{-100}^{100}[x^3]dx$$



      I have no idea how to go about it, can someone help me out










      share|cite|improve this question









      $endgroup$




      Let $[x]$ denote the greatest integer function, then evaluate



      $$int_{-100}^{100}[x^3]dx$$



      I have no idea how to go about it, can someone help me out







      calculus integration definite-integrals






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 17 at 14:27









      user601297user601297

      37119




      37119




      closed as off-topic by RRL, Alexander Gruber Jan 17 at 23:21


      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, Alexander Gruber

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







      closed as off-topic by RRL, Alexander Gruber Jan 17 at 23:21


      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, Alexander Gruber

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






















          1 Answer
          1






          active

          oldest

          votes


















          4












          $begingroup$

          Hint: If $ninmathbb Z$, then$$int_{sqrt[3]n}^{sqrt[3]{n+1}}lfloor x^3rfloor,mathrm dx=int_{sqrt[3]n}^{sqrt[3]{n+1}}n,mathrm dx=ntimesleft(sqrt[3]{n+1}-sqrt[3]nright).$$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Are you saying that between -2 to -1 the function will just be -2 and so on???
            $endgroup$
            – user601297
            Jan 17 at 17:47










          • $begingroup$
            Well… yes, I am! (Well, not quite. It will be $-8$ there.)
            $endgroup$
            – José Carlos Santos
            Jan 17 at 17:57










          • $begingroup$
            I’m sorry I don’t get how it will be -8, can you elaborate please
            $endgroup$
            – user601297
            Jan 17 at 17:58










          • $begingroup$
            There was an error in my answer and I've edited it. What do you think now?
            $endgroup$
            – José Carlos Santos
            Jan 17 at 18:04










          • $begingroup$
            Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
            $endgroup$
            – user601297
            Jan 17 at 18:05


















          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          4












          $begingroup$

          Hint: If $ninmathbb Z$, then$$int_{sqrt[3]n}^{sqrt[3]{n+1}}lfloor x^3rfloor,mathrm dx=int_{sqrt[3]n}^{sqrt[3]{n+1}}n,mathrm dx=ntimesleft(sqrt[3]{n+1}-sqrt[3]nright).$$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Are you saying that between -2 to -1 the function will just be -2 and so on???
            $endgroup$
            – user601297
            Jan 17 at 17:47










          • $begingroup$
            Well… yes, I am! (Well, not quite. It will be $-8$ there.)
            $endgroup$
            – José Carlos Santos
            Jan 17 at 17:57










          • $begingroup$
            I’m sorry I don’t get how it will be -8, can you elaborate please
            $endgroup$
            – user601297
            Jan 17 at 17:58










          • $begingroup$
            There was an error in my answer and I've edited it. What do you think now?
            $endgroup$
            – José Carlos Santos
            Jan 17 at 18:04










          • $begingroup$
            Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
            $endgroup$
            – user601297
            Jan 17 at 18:05
















          4












          $begingroup$

          Hint: If $ninmathbb Z$, then$$int_{sqrt[3]n}^{sqrt[3]{n+1}}lfloor x^3rfloor,mathrm dx=int_{sqrt[3]n}^{sqrt[3]{n+1}}n,mathrm dx=ntimesleft(sqrt[3]{n+1}-sqrt[3]nright).$$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Are you saying that between -2 to -1 the function will just be -2 and so on???
            $endgroup$
            – user601297
            Jan 17 at 17:47










          • $begingroup$
            Well… yes, I am! (Well, not quite. It will be $-8$ there.)
            $endgroup$
            – José Carlos Santos
            Jan 17 at 17:57










          • $begingroup$
            I’m sorry I don’t get how it will be -8, can you elaborate please
            $endgroup$
            – user601297
            Jan 17 at 17:58










          • $begingroup$
            There was an error in my answer and I've edited it. What do you think now?
            $endgroup$
            – José Carlos Santos
            Jan 17 at 18:04










          • $begingroup$
            Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
            $endgroup$
            – user601297
            Jan 17 at 18:05














          4












          4








          4





          $begingroup$

          Hint: If $ninmathbb Z$, then$$int_{sqrt[3]n}^{sqrt[3]{n+1}}lfloor x^3rfloor,mathrm dx=int_{sqrt[3]n}^{sqrt[3]{n+1}}n,mathrm dx=ntimesleft(sqrt[3]{n+1}-sqrt[3]nright).$$






          share|cite|improve this answer











          $endgroup$



          Hint: If $ninmathbb Z$, then$$int_{sqrt[3]n}^{sqrt[3]{n+1}}lfloor x^3rfloor,mathrm dx=int_{sqrt[3]n}^{sqrt[3]{n+1}}n,mathrm dx=ntimesleft(sqrt[3]{n+1}-sqrt[3]nright).$$







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Jan 17 at 18:03

























          answered Jan 17 at 14:32









          José Carlos SantosJosé Carlos Santos

          163k22131234




          163k22131234












          • $begingroup$
            Are you saying that between -2 to -1 the function will just be -2 and so on???
            $endgroup$
            – user601297
            Jan 17 at 17:47










          • $begingroup$
            Well… yes, I am! (Well, not quite. It will be $-8$ there.)
            $endgroup$
            – José Carlos Santos
            Jan 17 at 17:57










          • $begingroup$
            I’m sorry I don’t get how it will be -8, can you elaborate please
            $endgroup$
            – user601297
            Jan 17 at 17:58










          • $begingroup$
            There was an error in my answer and I've edited it. What do you think now?
            $endgroup$
            – José Carlos Santos
            Jan 17 at 18:04










          • $begingroup$
            Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
            $endgroup$
            – user601297
            Jan 17 at 18:05


















          • $begingroup$
            Are you saying that between -2 to -1 the function will just be -2 and so on???
            $endgroup$
            – user601297
            Jan 17 at 17:47










          • $begingroup$
            Well… yes, I am! (Well, not quite. It will be $-8$ there.)
            $endgroup$
            – José Carlos Santos
            Jan 17 at 17:57










          • $begingroup$
            I’m sorry I don’t get how it will be -8, can you elaborate please
            $endgroup$
            – user601297
            Jan 17 at 17:58










          • $begingroup$
            There was an error in my answer and I've edited it. What do you think now?
            $endgroup$
            – José Carlos Santos
            Jan 17 at 18:04










          • $begingroup$
            Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
            $endgroup$
            – user601297
            Jan 17 at 18:05
















          $begingroup$
          Are you saying that between -2 to -1 the function will just be -2 and so on???
          $endgroup$
          – user601297
          Jan 17 at 17:47




          $begingroup$
          Are you saying that between -2 to -1 the function will just be -2 and so on???
          $endgroup$
          – user601297
          Jan 17 at 17:47












          $begingroup$
          Well… yes, I am! (Well, not quite. It will be $-8$ there.)
          $endgroup$
          – José Carlos Santos
          Jan 17 at 17:57




          $begingroup$
          Well… yes, I am! (Well, not quite. It will be $-8$ there.)
          $endgroup$
          – José Carlos Santos
          Jan 17 at 17:57












          $begingroup$
          I’m sorry I don’t get how it will be -8, can you elaborate please
          $endgroup$
          – user601297
          Jan 17 at 17:58




          $begingroup$
          I’m sorry I don’t get how it will be -8, can you elaborate please
          $endgroup$
          – user601297
          Jan 17 at 17:58












          $begingroup$
          There was an error in my answer and I've edited it. What do you think now?
          $endgroup$
          – José Carlos Santos
          Jan 17 at 18:04




          $begingroup$
          There was an error in my answer and I've edited it. What do you think now?
          $endgroup$
          – José Carlos Santos
          Jan 17 at 18:04












          $begingroup$
          Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
          $endgroup$
          – user601297
          Jan 17 at 18:05




          $begingroup$
          Yup definitely makes sense now, your previous answer i think would be correct if the power was 1.
          $endgroup$
          – user601297
          Jan 17 at 18:05



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