So this seems to be a pretty straightforward question but I keep getting the arc length to be 0 and I redid this question many times..(adsbygoogle = window.adsbygoogle || []).push({});

Find the length of the parametrized curve given by

x(t) =[tex]t^{2}-8t + 24[/tex]

y(t) =[tex]t^{2}-8t -7 [/tex]

How many units of distance are covered by the point P(t) =(x(t), y(t)) between t=0, and t =8?

So my first step of course is to find dx/dt and dy/dt

[tex]\frac{dx}{dt}=2t-8[/tex]

[tex]\frac{dy}{dt}=2t-8[/tex]

Then set up the arc length equation

arc length = [tex]\int^{8}_{0}\sqrt{{\frac{dx}{dt}}^2+{\frac{dy}{dt}}^2}dt[/tex]

= [tex]\int^{8}_{0}\sqrt{{(2t-8)}^2+{(2t-8)}^2}dt[/tex]

= [tex]\int^{8}_{0}\sqrt{2{(2t-8)}^2}dt[/tex]

= [tex]\int^{8}_{0}\sqrt{2}(2t-8)dt[/tex]

=[tex]\sqrt{2}\int^{8}_{0}(2t-8)dt[/tex]

=[tex]\sqrt{2}\left[{t}^2-8t\right]^{8}_{0}dt[/tex]

Which give me an answer of zero when the answer is suppose to be 45.2548.

What I am doing wrong? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# What I am doing wrong? arc length of parametric functions

**Physics Forums | Science Articles, Homework Help, Discussion**