Find the error?

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 2sin$^2$ t, y = 2cos$^2$ t, 0 ≤ t ≤ 4π

I can't see what I did wrong here, posting image below. Any idea @TuringTest? The derivatives look ok...

Question

Find the error?

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 2sin$^2$ t,    y = 2cos$^2$ t,    0 ≤ t ≤ 4π

I can't see what I did wrong here, posting image below.  Any idea @TuringTest?  The derivatives look ok...

anonymous · Answer

attachment

anonymous · Answer

*Fixed the formatting syntax in the question

experimentx · Answer

http://www.wolframalpha.com/input/?i=8pi

anonymous · Answer

It's a full two revolutions, obviously.  What stumps me is what I could have done incorrect here when the other problem around it are ok...

*goes to see your link*

anonymous · Answer

8$\pi$?  o_O  What about it?

experimentx · Answer

why ... what is the answer?

anonymous · Answer

A smart way to see this problem is check that $$x ^{2}+y^{2}=4$$. This is an equation for the circunference with radius R=2. Since $$4 \pi $$ means two revolutions, the length of the circunference is  $$S=2\pi R$$ then the distance traveled is $$8\pi $$. Note that the displacement is zero, because the initial and end position are same while the distance traveled is not zero in this case.