- #1
eoghan
- 207
- 7
Hi all!
I have to find the length of the cycloid given by:
x(t)=t-sint
y(t)=1-cost
I did so:
length=[tex]\int\sqrt{1-cos^2 t -2cost + sin^2 t}[/tex]dt from 0 to 2p
[tex]\sqrt{2}\int\sqrt{1-cos t}[/tex]dt from 0 to 2p
with the substitution w=cost I get:
length=[tex]2\sqrt{2}\int\frac{dw}{2\sqrt{1+w}}[/tex]dw from 1 to 1 (cos0=cos2p=1)
Here's the problem: any integral from 1 to 1 is 0! But the cycloid has length=8
Where am I wrong?
I have to find the length of the cycloid given by:
x(t)=t-sint
y(t)=1-cost
I did so:
length=[tex]\int\sqrt{1-cos^2 t -2cost + sin^2 t}[/tex]dt from 0 to 2p
[tex]\sqrt{2}\int\sqrt{1-cos t}[/tex]dt from 0 to 2p
with the substitution w=cost I get:
length=[tex]2\sqrt{2}\int\frac{dw}{2\sqrt{1+w}}[/tex]dw from 1 to 1 (cos0=cos2p=1)
Here's the problem: any integral from 1 to 1 is 0! But the cycloid has length=8
Where am I wrong?