Question

Find the arc length of the curve e^ti + e^t cos(t)j + e^t sin(t)k where 0 ≤ t ≤ 2π.

Answer 1

So I used the arc length formula \[\int\limits_{0}^{2\pi}\sqrt{1+(dy/dx)^2}\]

Answer 2

\[\int\limits_{0}^{2\pi}\sqrt{\left(\frac{d x}{dt}\right)^2+\left(\frac{d y}{dt}\right)^2+\left(\frac{d z}{dt}\right)^2}dt\]

Answer 3

\[\int\limits_{0}^{2\pi}\sqrt{(e^t)^2+(e^tcost-e^tsint)^2+(e^tsint+e^tsint)^2}dx\]

Answer 4

yay, thank you!

Answer 5

\[\int\limits_{0}^{2\pi}\sqrt{(e^t)^2+(e^t\cos(t)-e^t\sin(t))^2+(e^t\sin(t)+e^t\cos(t))^2}dt\]

Answer 6

yeah, I realized my mistake when I punched it into my calculator. I got 925.766 or \[\sqrt{3}(e ^{2\pi}-1)\] thank you!!