Question

http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36-IMG004.png

I would like a hint please.

Answer 1

My hint is this:
top curve minus bottom curve

Answer 2

Not good enough. I already knew that. If I did not even know that, I would not have enough got any text in that answer box. @SmoothMath

Answer 3

Well, what part are you struggling with?

Answer 4

Getting rid of the absolute value.

Answer 5

Have you drawn the curves yet? Have you figured out where they cross each other on that interval?

Answer 6

No, that is the part I am having trouble with.

Answer 7

The area is divided into 2 regions, which is positive on [ 0, pi/6] and negative on [ pi/6, pi/2 ].

Answer 8

How did you find that out?

Answer 9

You know what I was doing wrong?
I was equating the two equations.

When I got to this part:

2sin^2(x) + sinx - 1 = 0, I let a = sinx

Then, I kept getting a = 1/2 and didn't understand when I set up the intervals what I was doing wrong. Then, I realized THAT I HAVE TO SUB BACK IN!

Answer 10

Therefore, I would get pi/6, like how you guys are getting

Answer 11

Those are your two curves. On the interval 0 to pi/2, sin(x) goes from 0 to 1
and cos(2x) goes from 1 to 0 and then to -1.