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Question

Find the arc length of the curve
π‘₯(𝑑)=cos𝑑+𝑑sin𝑑, 0β‰€π‘‘β‰€πœ‹/2
𝑦(𝑑) = sin 𝑑 βˆ’ 𝑑 cos 𝑑 ^2
9 years ago

Answers

Steve
(ds)^2 = (dx/dt)^2 + (dy/dt)^2
= (-sint + sint + tcost)^2 + (cost - cost + tsint)^2
= t^2cos^2(t) + t^2sin^2(t)
= t^2
so,

ds = dt

that's pretty easy to integrate, right?

Hmmm. I missed that ^2 hanging out there. Is

y(t) = sint - t(cost)^2
or
y(t) = sint - tcos(t^2)?

In either case, adjust the expression for ds above.
9 years ago

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