Originally Posted by
MechEng
Good afternoon,
I am working on finding the length of Archimedes Spiral
$\displaystyle r=\theta$
for... $\displaystyle 0\leq\theta\leq2\pi$.
I think I may be doing something wrong. This is what I'm getting:
$\displaystyle r=\theta$
$\displaystyle \displaystyle\huge\frac{dr}{d\theta}=1$
$\displaystyle \displaystyle\int_{0}^{2\pi}\sqrt{r^2+\left(\frac{ dr}{d\theta}\right)^2}\ d\theta$
Shouldn't you have been working from the above ?
I have evaluated this to:
$\displaystyle \displaystyle\frac{\theta}{2}\sqrt{\theta^2-1}-\frac{ln(\theta+\sqrt{\theta^2-1}}{2}|_{0}^{2\pi}$
When I try to wrap this up by plugging in my terminals... I get a mess. Is this right?
$\displaystyle \displaystyle\pi\sqrt{(2\pi)^2-1}-\frac{ln(\2\pi+\sqrt{(2\pi)^2-1})}{2}$