## anonymous 5 years ago Need help finding the distance traveled by a particle that travels along these parametric curves: x=9-3cos^(2)(6t) y=5sin^(2)(6t) from −2pi less than or equal to t less than or equal to 3pi

1. anonymous

I get $\sqrt{4896}\int\limits_{-2\pi}^{3\pi}\left| \sin(6t)\cos(6t) \right|dt$

2. anonymous

Did I set it up wrong?

3. anonymous

I would use the arc length formula here -> the integral of sqrt( 1 + (dy/dx)^2) from -2pi to 3pi

4. anonymous

Because it's parametric how would I do that?

5. anonymous

right, it needs to be modified a bit for parametric curves. It should be the integral of the square root of (dx/dt)^2 + (dy/dt)^2 from -2pi to 3pi

6. anonymous

L=$\int\limits_{a}^{b}\sqrt{(dx/dt)^2 + (dy/dt)^2 dt}$

7. anonymous

yes, like that

8. anonymous

Well, I get the previous answer I posted ^

9. anonymous

Idk, maybe my calculator is rounding it to an answer that doesn't work.

10. anonymous

I end up getting 351.5278214

11. anonymous

You should get the equation: integral from -2pi to 3pi of sqrt((6sin(12t))^2 + (30sin(12t))^2)

12. anonymous

I get 305.941

13. anonymous

Oh.. I kept getting something else. I have no idea. But Thanks, honestly.

14. anonymous

no problem