Homework Help: Area under a graph

1. Aug 20, 2010

tomwilliam

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. Aug 20, 2010

Whitishcube

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.

3. Aug 20, 2010

ehild

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

ehild

4. Aug 20, 2010

tomwilliam

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.

5. Aug 20, 2010

l'Hôpital

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?

6. Aug 20, 2010

tomwilliam

Ah yes, I see now.
Thanks all.