1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook