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Math Help - Integration Problem to solve. Cannot quite understand what's required.

  1. #1
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    Integration Problem to solve. Cannot quite understand what's required.

    Hi MHF!

    The final problem in an assignment I have is making absolutely no sense, mainly because it sounds technical and I can't determine what's required of me.

    The following is the problem:

    A current:
    i =  45 sin(100\pi t)
    amperes is applied across an electric circuit. Determine its mean and r.m.s values each correct to 4s.f., over the range t=0 to t=10 ms.
    So, first up, because of the theme of the assignment I'm assuming integration is involved with limits ranging from 0 to 0.01.

    Integrating 45sin(100PI t) dt would result in \frac {- 45cos(100\pi t)}{ 100PI} (Correct me if I'm wrong, I believe chain rule is as in differentiation as integration, however it's in division instead of multiplication).

    Finally, the main problem is, I need the mean and r.m.s, which I have no clue what it equates to from the values I find. Can someone please help clarify this problem?

    EDIT: Just remembered, since this is what previous problems involved in the assignment, should I use the Trapezium/Mid-ordinate/Simpson's Rule instead by any chance, since Mean probably means average and r.m.s might have something to do with that?

    Thanks and regards,

    Lupo
    Last edited by Luponius; May 14th 2013 at 01:30 AM.
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  2. #2
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    Re: Integration Problem to solve. Cannot quite understand what's required.

    Hey Luponius.

    Hint: The RMS is going to be according to the wiki

    https://en.wikipedia.org/wiki/Root_m...are#Definition
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  3. #3
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    Re: Integration Problem to solve. Cannot quite understand what's required.

    Thanks for the hint, reading through it I'm positive it doesn't sound familiar at all, we haven't done any of this in class specifically.

    If I understood correctly I'm to acquire the mean initially. This is done by doing an integration between 0 and 0.01 of 45sin(100\pi t). The result will be the mean value or average?
    Following that I'll square root the answer?

    Can you please confirm?

    Regards,

    Lupo
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  4. #4
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    Re: Integration Problem to solve. Cannot quite understand what's required.

    The mean value is calculated by integrating the function over the given range and then dividing that result by the width of the interval.

    To calculate the R.M.S. value,
    (1) square the function;
    (2) find the mean value (of the square of the function) as above over the given interval;
    (3) take the square root of this mean value.
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  5. #5
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    Re: Integration Problem to solve. Cannot quite understand what's required.

    So for the mean: Integrate between 0 to 0.01 and divide answer by 0.01 since that's the width of the interval in seconds. Mean acquired.

    Now the R.M.S steps are confusing me, square the function... am I to raise the power of f(i) to 2 or something else?
    Next up on step two you metion I find the mean by integrating the squared function, which would not be the same as a standard definite integration.
    I then square root the mean, this I find fine, but do I actually do f(i) ^ 2 first before doing any of the rest or do I not?

    Sorry if I'm being slow, I'm seriously confused, every other question leading to this was straightforward definite/indefinite integration and this popped up and I'm completely lost with the english of it.

    Regards,

    Lupo.
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  6. #6
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    Re: Integration Problem to solve. Cannot quite understand what's required.

    to update this is solved, thank you very much BobP, chiro. Greatly appreciate your assistance!

    Thanks once again and regards,

    Lupo!
    =]
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