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Integral calculus

  1. Jun 28, 2012 #1
    1. The problem statement, all variables and given/known data

    A generated AC voltage has a value given by V = 4cos2θ.

    You will need to use the identity cos^2⁡θ = 1/2(1+cos2θ)


    a) Find the mean value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus

    b) Find the r.m.s. value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus



    2. Relevant equations



    3. The attempt at a solution


    4∫cos2x dx u = 2x du= 2dx du/2 = dx


    4∫ cos u du

    2 sin 2x +c



    What is next now?
     
  2. jcsd
  3. Jun 28, 2012 #2

    SammyS

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    Find the average over a full cycle.

    The average (mean) value of function f(x) over the interval [a, b] is given by

    [itex]\displaystyle f_\text{Mean}=\frac{\displaystyle \int_a^b{f(x)\,dx}}{b-a}\ .[/itex]
     
  4. Jun 29, 2012 #3

    Where is the interval?

    Is this f(x)? = 2 sin 2x +c
     
  5. Jun 29, 2012 #4
    Hello maali5,
    The interval has been quoted in your question right?
    (0 ≤ θ ≤ 2π)
    You have to have a definite integral right?So you will have to plug in these limits.And then the use the expression quoted by SammyS with these limits.

    regards
    Yukoel
     
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