Thread: U-Substitution with du=0 View Single Post

## U-Substitution with du=0

1. The problem statement, all variables and given/known data

I am trying to prove that the length of a helix can be represented by $2\pi=\sqrt{a^2+b^2}$

2. Relevant equations

3. The attempt at a solution

I have the following so far:

If the helix can be represented by $h(t)=a\cdot cos(t)+a\cdot sin(t)+b(t)$

Then the length is:
$$\int_{0}^{2\pi}\sqrt{(-a\cdot sin(t))^2+(a\cdot cos(t))^2+b^2}\;\: dt$$

My problem comes when integrating this. If I use the stuff in the root as u and do u-substitution, then du equals 0dt:

$$u=a^2sin^(t)+a^2cos^2(t)+b^2$$
$$du=(a^2sin(2t)-a^2sin(2t))dt=0dt$$

My logic fails me when figuring out how to continue from there. I need to somehow represent 1dt. How do I do this?

Help would be awesome!

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