anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I get \[\sqrt{4896}\int\limits_{-2\pi}^{3\pi}\left| \sin(6t)\cos(6t) \right|dt\]
anonymous
  • anonymous
Did I set it up wrong?
anonymous
  • anonymous
I would use the arc length formula here -> the integral of sqrt( 1 + (dy/dx)^2) from -2pi to 3pi

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anonymous
  • anonymous
Because it's parametric how would I do that?
anonymous
  • 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
anonymous
  • anonymous
L=\[\int\limits_{a}^{b}\sqrt{(dx/dt)^2 + (dy/dt)^2 dt}\]
anonymous
  • anonymous
yes, like that
anonymous
  • anonymous
Well, I get the previous answer I posted ^
anonymous
  • anonymous
Idk, maybe my calculator is rounding it to an answer that doesn't work.
anonymous
  • anonymous
I end up getting 351.5278214
anonymous
  • anonymous
You should get the equation: integral from -2pi to 3pi of sqrt((6sin(12t))^2 + (30sin(12t))^2)
anonymous
  • anonymous
I get 305.941
anonymous
  • anonymous
Oh.. I kept getting something else. I have no idea. But Thanks, honestly.
anonymous
  • anonymous
no problem

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