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: Help with integration

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate and give an exact answer.

    [tex]$\int_{0}^{\frac{Pi}{2}\right)}cos^2(2*Pi*n*x)dx[/tex] where n is a positive integer.

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure how to write a Riemann Sum in latex code, so I'll be using "S" as the notation for the Riemann Sum (i=1, n): f(x_i)*(b-a)/n

    I used the limit as n -> oo definition of an integral:


    Next I substituted the values of [tex]x_i[/tex]:


    Then evaluated [tex]f(x_i)[/tex]:


    Here is where i get a bit confused. In the example with n-subintervals that I worked through in my book, it substituted the value of the Riemann sum of i using the power of sums formula, however, I end up with "i" inside of the cosine function, and am not sure how to finish evaluating the integral.

    Other examples in the book had the value of n defined, thus making the integration process much more simple.

    Am I even doing the right thing? Bare with me, my integration is self taught.
  2. jcsd
  3. Oct 2, 2009 #2


    User Avatar
    Science Advisor

    Why are you trying to change to Riemann sums? That is, at best, a very difficult way of evaluating integrals! (Though excellent for thinking how to set up integrals for applications.)

    Do you know the anti-derivatives of sine and cosine themselves? If so you can use the trig identity [itex]cos^2(\theta)= (1/2)(1+ cos(2\theta)[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook