MHB Interval for the Length of an Arc

[ineedhelpnow]

find the length of an arc of a helix r(t)=(sint,cost,t) from the point (0,2,0) to (0,5,2pi)

would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.

 

[I like Serena]

find the length of an arc of a helix r(t)=(sin2t,cos2t,t) from the point (0,2,0) to (0,5,2pi)

would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.

Yes.

 

[ineedhelpnow]

really? is this right?
View attachment 3246

 

[I like Serena]

really? is this right?

It would be right... but I'm only just now noticing that your function is not a helix.
How does it get to $y=5$? (Wondering)

 

[ineedhelpnow]

ok ILS ima let you in on a little secret (i don't really remember the points. all i remember are the z coordinates 0 and 2pi) but it was a helix for sure. it was probably 5 instead of 2. i don't know i can't remember. i don't want to say i made them up but I am going to saaaaay improvised.

 

[I like Serena]

ok ILS ima let you in on a little secret (i don't really remember the points. all i remember are the z coordinates 0 and 2pi)

Okay...
How about $r(t)=\left(\frac{3t}{2\pi}\sin(t),\ 2+\frac{3t}{2\pi}\cos(t),\ t\right)$?

 

[ineedhelpnow]

what about it?
you would differentiate and pull out a common factor and simplify the sin and cos to 1. and then add the extra 1 and take the square root.

 

[I like Serena]

what about it?
you would differentiate and pull out a common factor and simplify the sin and cos to 1. and then add the extra 1 and take the square root.

Did you really differentiate it?
How about the factor $t$ that is in both the x-coordinate and the y-coordinate (which is an integral part of a helix)?

 

[ineedhelpnow]

factor it out before you differentiate.

 

[I like Serena]

factor it out before you differentiate.

Can you show that?

Edit: Perhaps I should say: you can't.

 

[ineedhelpnow]

why can't it be factored out?

 

[I like Serena]

why can't it be factored out?

I'm not entirely sure what you mean, but I'm going out on a limb and say: no, it can't be factored out.

What is the derivative of $t \cos t$?

 

[ineedhelpnow]

cos t - t*sin t

 

[I like Serena]

cos t - t*sin t

There you go!
No factoring out before the differentiation.

 

[ineedhelpnow]

what about it?
you would differentiate and pull out a common factor and simplify the sin and cos to 1. and then add the extra 1 and take the square root.

:D soooo you can just do what i said earlier. by differentiating. pulling out a common factor of 3/2pi and---- oh i see what i did wrong. (Giggle) made a mistake with the differentiating part.