Continuous summation of a function

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1
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I have a simple function:



func =x Sin[π x]^2


This creates a curve that oscillates between 0 and values that increase linearly with x.



I want to create a continuous sum of func, so that incremental increases in x add to the running total. The result would be a continuously rising curve, with periods of rapid growth interspersed with periods of something closer to a plateau, based on the frequency of the Sin function.



How do I do this?






calculus-and-analysis function-construction







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  • 1




    f=Integrate[x Sin[Pi x]^2,x] ; Plot[f,x,0,4Pi]
    – Bill
    4 hours ago










  • How does a "continous summation" differ from an integral?
    – Î‘λέξανδρος Ζεγγ
    3 hours ago














up vote
1
down vote

favorite












I have a simple function:



func =x Sin[π x]^2


This creates a curve that oscillates between 0 and values that increase linearly with x.



I want to create a continuous sum of func, so that incremental increases in x add to the running total. The result would be a continuously rising curve, with periods of rapid growth interspersed with periods of something closer to a plateau, based on the frequency of the Sin function.



How do I do this?






calculus-and-analysis function-construction







share|improve this question



















  • 1




    f=Integrate[x Sin[Pi x]^2,x] ; Plot[f,x,0,4Pi]
    – Bill
    4 hours ago










  • How does a "continous summation" differ from an integral?
    – Î‘λέξανδρος Ζεγγ
    3 hours ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I have a simple function:



func =x Sin[π x]^2


This creates a curve that oscillates between 0 and values that increase linearly with x.



I want to create a continuous sum of func, so that incremental increases in x add to the running total. The result would be a continuously rising curve, with periods of rapid growth interspersed with periods of something closer to a plateau, based on the frequency of the Sin function.



How do I do this?






calculus-and-analysis function-construction







share|improve this question















I have a simple function:



func =x Sin[π x]^2


This creates a curve that oscillates between 0 and values that increase linearly with x.



I want to create a continuous sum of func, so that incremental increases in x add to the running total. The result would be a continuously rising curve, with periods of rapid growth interspersed with periods of something closer to a plateau, based on the frequency of the Sin function.



How do I do this?






calculus-and-analysis function-construction




calculus-and-analysis function-construction






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 37 mins ago









m_goldberg

82.2k869190




82.2k869190










asked 4 hours ago









Richard Burke-Ward

3487




3487







  • 1




    f=Integrate[x Sin[Pi x]^2,x] ; Plot[f,x,0,4Pi]
    – Bill
    4 hours ago










  • How does a "continous summation" differ from an integral?
    – Î‘λέξανδρος Ζεγγ
    3 hours ago












  • 1




    f=Integrate[x Sin[Pi x]^2,x] ; Plot[f,x,0,4Pi]
    – Bill
    4 hours ago










  • How does a "continous summation" differ from an integral?
    – Î‘λέξανδρος Ζεγγ
    3 hours ago







1




1




f=Integrate[x Sin[Pi x]^2,x] ; Plot[f,x,0,4Pi]
– Bill
4 hours ago




f=Integrate[x Sin[Pi x]^2,x] ; Plot[f,x,0,4Pi]
– Bill
4 hours ago












How does a "continous summation" differ from an integral?
– Î‘λέξανδρος Ζεγγ
3 hours ago




How does a "continous summation" differ from an integral?
– Î‘λέξανδρος Ζεγγ
3 hours ago










1 Answer
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The "continuous sum" of a function is it's integral so



f[x_] := x Sin[Pi x]^2
sumf = Integrate[f[x], x];
Plot[f[x], sumf, x, 0, 2 Pi]


enter image description here






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    1 Answer
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    up vote
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    down vote













    The "continuous sum" of a function is it's integral so



    f[x_] := x Sin[Pi x]^2
    sumf = Integrate[f[x], x];
    Plot[f[x], sumf, x, 0, 2 Pi]


    enter image description here






    share|improve this answer
























      up vote
      2
      down vote













      The "continuous sum" of a function is it's integral so



      f[x_] := x Sin[Pi x]^2
      sumf = Integrate[f[x], x];
      Plot[f[x], sumf, x, 0, 2 Pi]


      enter image description here






      share|improve this answer






















        up vote
        2
        down vote










        up vote
        2
        down vote









        The "continuous sum" of a function is it's integral so



        f[x_] := x Sin[Pi x]^2
        sumf = Integrate[f[x], x];
        Plot[f[x], sumf, x, 0, 2 Pi]


        enter image description here






        share|improve this answer












        The "continuous sum" of a function is it's integral so



        f[x_] := x Sin[Pi x]^2
        sumf = Integrate[f[x], x];
        Plot[f[x], sumf, x, 0, 2 Pi]


        enter image description here







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 4 hours ago









        Rohit Namjoshi

        1737




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