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U-Substitution with du=0

  • Thread starter BraedenP
  • Start date
  • #1
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Homework Statement



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

Homework Equations





The Attempt at a Solution



I have the following so far:

If the helix can be represented by [itex]h(t)=a\cdot cos(t)+a\cdot sin(t)+b(t)[/itex]

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

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

[tex]u=a^2sin^(t)+a^2cos^2(t)+b^2[/tex]
[tex]du=(a^2sin(2t)-a^2sin(2t))dt=0dt[/tex]

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!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
If your du comes out to be zero, then u must be a constant. What constant is it? Use some trig to simplify your u.
 
  • #3
gb7nash
Homework Helper
805
1
You don't need u-substitution for this problem. Here's why:

Before you try taking the integral, inside the square root, you have a2sin2t + a2cos2t. Factor the a2 out of both of them. What happens?
 
  • #4
96
0
Yep, was definitely over-thinking it. Thanks guys :)
 

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