## agentx5 2 years ago 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...

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1. agentx5

2. agentx5

*Fixed the formatting syntax in the question

3. experimentX
4. agentx5

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*

5. agentx5

8$$\pi$$? o_O What about it?

6. experimentX

why ... what is the answer?

7. amorim.fatec

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.