Mathematics, 12.03.2020 03:10 ecenteno2004
Find the arc length parameter along the given curve from the point where t=0 by evaluating the integral s(t)=lv(t)ldt
Then find the length of indicated portion of the curve r(t)= 5costi+5sintj+8tk, where 0<_t<_pi
The arc length parameter along the curve, starting at t=0 is s(t)=. (Type exact answers, using radicals as needed)
The length of the indicated portion of the curve is L=___. (Type exact answers, using radicals and Pi as needed)
Find the arc length parameter along the given curve from the point where t=0 by evaluating the integral s(t)=lv(t)ldt
Then find the length of indicated portion of the curve r(t)=(2e^tcost)i+(2e^tsint)j-2e^tk, -ln4<_t<_0 s(t)=__ (Type exact answers, using radicals as needed)
The length of rage indicated portion of the curve is __ units. (Type exact answers, using radicals as needed)
Answers: 2
where 
with respect to 
![s(t)=\int\limits^b_a|v(\tau)|dt\\\\=\int\limits^{\frac{\pi}{6}}_a\sqrt{181}dt\, since\, |v|=|r'(t)|\, or\, |v|=\sqrt{181}\\\\=\sqrt{181}[t]\limits^{\frac{\pi}{6}}_0\\\\=\sqrt{181}[\frac{\pi}{6}-0]\\\\=\frac{\sqrt{181\times \pi}}{6}=7.0443](/tpl/images/0544/2333/54026.png)
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