Mathematics, 17.07.2021 06:40 zack66828
Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1
Answers: 3
![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](/tpl/images/1395/5319/4bc1d.png)
![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](/tpl/images/1395/5319/fb0e0.png)
![\displaystyle AL = \int\limits^b_a {\sqrt{[i'(t)]^2 + [j'(t)]^2 + [k'(t)]^2}} \, dt](/tpl/images/1395/5319/9efe3.png)
Substitute in variables [Arc Length Formula - Vector]: ![\displaystyle AL = \int\limits^1_0 {\sqrt{\bigg[\frac{d}{dt}[10\sqrt{2}t \textbf i]\bigg]^2 + \bigg[\frac{d}{dt}[e^{10t} \textbf j]\bigg]^2 + \bigg[\frac{d}{dt}[e^{-10t} \textbf k ]\bigg]^2}} \, dt](/tpl/images/1395/5319/667ea.png)
[Integrand] Differentiate [Respective Differentiation Rules]: ![\displaystyle AL = \int\limits^1_0 {\sqrt{[10\sqrt{2} \textbf i]^2 + [10e^{10t} \textbf j]^2 + [-10e^{-10t} \textbf k]^2}} \, dt](/tpl/images/1395/5319/4b705.png)
[Integrand] Simplify: 
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Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1...
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