Question

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

Answer 1

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

Answer 2

Did I set it up wrong?

Answer 3

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

Answer 4

Because it's parametric how would I do that?

Answer 5

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

Answer 6

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

Answer 7

yes, like that

Answer 8

Well, I get the previous answer I posted ^

Answer 9

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

Answer 10

I end up getting 351.5278214

Answer 11

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

Answer 12

I get 305.941

Answer 13

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

Answer 14

no problem