Thread: U-Substitution with du=0 View Single Post
 P: 96 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!