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Thread: can anyone try this question?

  1. #1 can anyone try this question? 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    now this may seem like hmwrk, but it isn't, i was just going through past exam papers on integrating exponential function, and i cant get an answer to this;

    i)show that

    now i get this proving part but its the next part which is confusing;

    use the result from (i) to find

    i appreciate any help in solving this question, thank you


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  3. #2  
    Forum Masters Degree organic god's Avatar
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    well if d/dx(f(x)) = g(x)

    then the integral of g(x) = f(x)


    everything is mathematical.
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  4. #3  
    Ots
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    Quote Originally Posted by organic god
    well if d/dx(f(x)) = g(x)

    then the integral of g(x) = f(x)
    What O-god has said here almost has to be the point of the excercise so it leads one to believe that H-berg may have stated the problem wrong.
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  5. #4  
    Forum Masters Degree organic god's Avatar
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    What O-god has said here almost has to be the point of the excercise so it leads one to believe that H-berg may have stated the problem wrong.
    problem may not of been stated wrong, i guess the first part test if you can differentiate. and the second part is just a small rearrangement and a test of integration
    everything is mathematical.
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  6. #5  
    Ots
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    I guess what I was trying to say was that perhaps the problem was to differentiate and then integrate the result of the differentiation, which is kind of what your first response was suggesting. But that's not the problem H-berg presented. The problem H-berg presented has a pretty staightforward differentiation, but integrating lnx/x^3 looks like it will require more effort from me than I'm willing to give it. But I might be missing something too. Sometimes I'll not see a slick way to integrate something.
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  7. #6  
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    ∫(lnx/x^3) = -lnx/2x^2 right?
    correct me if im wrong, please
    maybe this helps
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  8. #7 Re: can anyone try this question? 
    Forum Radioactive Isotope MagiMaster's Avatar
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    Quote Originally Posted by Heinsbergrelatz
    now this may seem like hmwrk, but it isn't, i was just going through past exam papers on integrating exponential function, and i cant get an answer to this;

    i)show that

    now i get this proving part but its the next part which is confusing;

    use the result from (i) to find

    i appreciate any help in solving this question, thank you
    I think the point here is, you have and some function that can be decomposed into something like . Then, to integrate f, you can use the decomposition, the given differentiation and the fundamental theorem of calculus to solve the integral.
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  9. #8  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    to ots; trust me, im not wrong, i copied the exact question given from the CIE itself, so its either they are wrong which i hardly doubt it
    and to others, appreciate the suggestions
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  10. #9  
    Forum Masters Degree organic god's Avatar
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    ok as d/dx(ln x/x^2) = (1 - 2ln x)/x^3

    integrate both sides

    ln x/x^2 = int ((1 - 2 ln x)/x^3)

    the integral looks complicated but it can be split into two seperate integrals

    ln x/x^2 = int (1/x^3) + int (-2 ln x /x^3)

    so int (-2 ln x/x^3) = ln x/x^2 - int (1/x^3)

    so int ln x/x^3 = -1/2 ( ln x/x^2 - int (1/x^3))

    the LHS is the question and the right hand side ends up as follows

    = -1/2 (ln x/x^2 + 1/2x^2 + C)
    everything is mathematical.
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  11. #10  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    i really appreciate all of your answers,
    especially, to organic god, your solutions really pulled me off with this one thank you
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  12. #11  
    Ots
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    Quote Originally Posted by organic god
    ok as d/dx(ln x/x^2) = (1 - 2ln x)/x^3

    integrate both sides

    ln x/x^2 = int ((1 - 2 ln x)/x^3)

    the integral looks complicated but it can be split into two seperate integrals

    ln x/x^2 = int (1/x^3) + int (-2 ln x /x^3)

    so int (-2 ln x/x^3) = ln x/x^2 - int (1/x^3)

    so int ln x/x^3 = -1/2 ( ln x/x^2 - int (1/x^3))

    the LHS is the question and the right hand side ends up as follows

    = -1/2 (ln x/x^2 + 1/2x^2 + C)
    But what was to be integrated was ln x/ x^3, as put forth in the original post.
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  13. #12  
    Forum Masters Degree organic god's Avatar
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    But what was to be integrated was ln x/ x^3, as put forth in the original post.
    clearly im missing your point because i'm pretty sure the LHS of the equation is the integral of ln x/x^3

    really appreciate all of your answers,
    especially, to organic god, your solutions really pulled me off with this one thank you
    always happy to help
    everything is mathematical.
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  14. #13  
    Ots
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    Quote Originally Posted by organic god
    clearly im missing your point because i'm pretty sure the LHS of the equation is the integral of ln x/x^3
    Yes, I see how you worked your way down to it and the way you did all of this had to be the proper solution to the original problem.
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