# Math Help - Arc Length

1. ## Arc Length

Consider the path r(t) = (10t, 5t^2, 5lnt) defined for t > 0.
Find the length of the curve between the points (10, 5, 0) and (20, 20, 5 ln(2)).

Thanks

2. Originally Posted by jffyx
Consider the path r(t) = (10t, 5t^2, 5lnt) defined for t > 0.
Find the length of the curve between the points (10, 5, 0) and (20, 20, 5 ln(2)).

Thanks
$L = \int_{t=1}^{t=2} \sqrt{100 + 100t^2 + \frac{25}{t^2}} \, dt = \int_{t=1}^{t=2} \frac{1}{t} \sqrt{(10t^2 + 5)^2} \, dt = \, ....$

3. How did you determine the interval of integration?

4. the path r(t) = (10t, 5t^2, 5lnt) defined for t > 0.
Find the length of the curve between the points (10, 5, 0) and (20, 20, 5 ln(2)).
What value of t makes (10t, 5t^2, 5ln t) equal to (10, 5, 0)? What value of t makes (10t, 5t^2, 5 ln t) equal to (20, 20, 5 ln 2)?