Find the length of the curve. \vec{r}(t) =< 8t, t^2,

Danelle Albright

Danelle Albright

Answered question

2021-12-21

Find the length of the curve.
r(t)=<8t,t2,112t3>,0t1

Answer & Explanation

esfloravaou

esfloravaou

Beginner2021-12-22Added 43 answers

r(t)=<8,2t,312t2>
r(t)=<8,2t,14t2>
||r(t)||=(8)2+(2t)2+(14t2)2
||r(t)||=64+4t2+116t4
||r(t)||=116((6416)+64t2+t4)
||r(t)||=141024+64t2+t4
||r(t)||=14322+(232)t2+t4
||r(t)||=14(32+t2)2
||r(t)||=14|32+t2|
Now, t2 is always positive. So, (32+t2) is always positive.
Cheryl King

Cheryl King

Beginner2021-12-23Added 36 answers

Where is the second part of solution?
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

we know that, the length of the curve between t = 0 and t = 1 can be computed as
L=t=0t=1||r(t)||dtL=t=0t=114(32+t2)dtL=14t=0t=1(32+t2)dtL=14[32+t33]t=0t=1L=14[(32+13)(0+0)]L=14(32+13)L=14973L=9712

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