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: Area under a graph

  1. Aug 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region between x=-pi/6 and x=pi/4 above the x-axis and below the graph of:
    y=cos(2x)(8-cos(2x))


    2. Relevant equations



    3. The attempt at a solution
    I know I need to reformulate the expression somehow so that it is easier to integrate, and I'm guessing it's a double angle formula like:
    cos (2x) = 2 cos^2 x -1
    but I can't seem to bring it all together to find something I know how to integrate.
    Any hints? This is an assignment question, so I'd like to know how to do it properly. I've also changed a few of the values (but not the argument of the trig functions).
     
  2. jcsd
  3. Aug 20, 2010 #2
    good. so far youre off to a good start. use that trig identity and play around with it once you substitute that in your integral.
     
  4. Aug 20, 2010 #3

    ehild

    User Avatar
    Homework Helper

    You guess well, but use the formula in the opposite way, to make cos^2 (2x) disappear. You can integrate cos2x and cos4x.

    ehild
     
  5. Aug 20, 2010 #4
    I'm a little confused by that...if I use the formula the opposite way to get cos^2 to disappear, I get back to what I started with.
    At the moment I've changed the cos(2x) and expanded the brackets to get:

    16 cos^2 (x) - 7 - 4 cos^4 (x)

    I'm not sure if I'm any closer or not.
     
  6. Aug 20, 2010 #5
    You are thinking about it the wrong way. You have

    f(x) = 8 cos(2x) - cos^2 (2x)

    You could easily do u sub, so 8 cos(u) - cos^2(u). Integrating cos is easy, but what about cos^2?
     
  7. Aug 20, 2010 #6
    Ah yes, I see now.
    Thanks all.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook