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anonymous
 5 years ago
Need help finding the distance traveled by a particle that travels along these parametric curves:
x=93cos^(2)(6t)
y=5sin^(2)(6t)
from −2pi less than or equal to t less than or equal to 3pi
anonymous
 5 years ago
Need help finding the distance traveled by a particle that travels along these parametric curves: x=93cos^(2)(6t) y=5sin^(2)(6t) from −2pi less than or equal to t less than or equal to 3pi

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I get \[\sqrt{4896}\int\limits_{2\pi}^{3\pi}\left \sin(6t)\cos(6t) \rightdt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Did I set it up wrong?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I would use the arc length formula here > the integral of sqrt( 1 + (dy/dx)^2) from 2pi to 3pi

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Because it's parametric how would I do that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0L=\[\int\limits_{a}^{b}\sqrt{(dx/dt)^2 + (dy/dt)^2 dt}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, I get the previous answer I posted ^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Idk, maybe my calculator is rounding it to an answer that doesn't work.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I end up getting 351.5278214

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You should get the equation: integral from 2pi to 3pi of sqrt((6sin(12t))^2 + (30sin(12t))^2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh.. I kept getting something else. I have no idea. But Thanks, honestly.
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