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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

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    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.
     
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