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Math Help - RMS and integration

  1. #1
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    RMS and integration

    Hi,
    in a question of my assignment i was asked to find the integral of e^{-x/2}cos(2x) which I found it to be \frac{e^{-x/2}(8sin(2x)-2cos(2x))}{17} with Integration by parts that had to be done 2 times and finally with the reduction method. In the last part of the question he asks: "hence find the rms value of e^{-x/4}sinx. I noticed that this was already tackled in a step of the previous integration but I am not sure on the rms part. I am aware that the rms is the equivalent area. (equivalent D.C component) Can you please give me a hint or maybe post some good links to where I can understand the relation between rms and integration ?
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  2. #2
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    Quote Originally Posted by trojsi View Post
    Hi,
    in a question of my assignment i was asked to find the integral of e^{-x/2}cos(2x) which I found it to be \frac{e^{-x/2}(8sin(2x)-2cos(2x))}{17} with Integration by parts that had to be done 2 times and finally with the reduction method. In the last part of the question he asks: "hence find the rms value of e^{-x/4}sinx. I noticed that this was already tackled in a step of the previous integration but I am not sure on the rms part. I am aware that the rms is the equivalent area. (equivalent D.C component) Can you please give me a hint or maybe post some good links to where I can understand the relation between rms and integration ?
    The simple "average" value of a function f(x), for a< x< b is \frac{\int_a^b f(x)dx}{b- a}. I mention that to point out that it is a simple generalization the average of n numbers: instead of summing, we integrate, instead of dividing by the "size" of the set of numbers, we divide by the "size" of the interval.

    Similarly, the "root mean square" average of a list of n numbers is \sqrt{\frac{\sum a_n^2}{n}} so the "root mean square" average of a function is
    \sqrt{\frac{\int_a^b (f(x))^2 dx}{b- a}}.

    The square of e^{-x/4}sin x is, of course, e^{-x/2}sin^2 x= e^{-x/2}\left((1/2)(1- cos(2x)\right).
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  3. #3
    A Plied Mathematician
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    Is this "question of my assignment" for a grade?
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  4. #4
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    Question

    Actually the thing is that in class we didn't mention anything on integration and average.. and the question is part of a merit in the assignment.
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  5. #5
    A Plied Mathematician
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    What does "merit in the assignment" mean? Extra credit? Or just part of the normal grade?
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  6. #6
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    In our assignments we either get a pass, merit or a distinction so it is a type of grading criteria. Did I do something wrong by asking for this type of hint?

    thanks

    Brandon
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  7. #7
    A Plied Mathematician
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    It is forum policy not knowingly to help with any assignment that counts towards a grade. What you should do on the MHF is to ask questions similar, but not identical, to the questions you need to do for class. Make sense?
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  8. #8
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    Thanks. It does make sense but initially I only asked for some good links where i can understand the relationship better. Next time I'll try not to involve so much detail or discuss a similar question as advised. thanks again.
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