Integration over a curve question.
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Integration over a curve question.

[From: ] [author: ] [Date: 12-12-08] [Hit: ]
Perhaps, you had a typo.......
I am given a problem as follows,
Compute the length of the helix that wraps 5 times around the lateral side of a right circular cylinder of radius R and height H w/ a constant pitch (so each wrap rises the same direction up the cylinder)

The answer: Sqrt[ (10π R^2) + H^2 ]

My issue: Conceptually, so far we have been computing integrals over curves through breaking the curves into small pieces of the length ds (w/ is the magnitude of dr= (dx)i + (dy)j). Where other problems were straight forward given an equation, all I had to do was describe the length element in terms of one variable, however, I'm not sure how that problem is depicted in this problem, i do understand how if we were to set the integral up, it's bounds would be 0
Basically I'm looking for the framework behind coming up with this answer as can best be done on Yahoo answers....lol thanks in advance math friends

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This is more like a Calc 3 problem.

I will use variable t instead of x

the helix equation is:
r(t) =


L = ∫ || r(t) || dt, t = 0 to 5(2pi)

L = ∫ sqrt[ (-Rsint)^2 + (R cost)^2 + ( H/(10pi))^2 ] dt

L = ∫ sqrt[ R^2 + (H/(10pi))^2 ] dt

L = sqrt[ R^2 + (H/(10pi))^2 ] t

evaluating the limits
L = sqrt[ R^2 + (H/(10pi))^2 ] (10pi)
L = sqrt ( (10pi R)^2 + H^2 )

Perhaps, you had a typo. You had 10pi (R^2) while I had (10pi R)^2
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