Finding Arc Length of c between (2,1,0) and (4,4,log2)

[aligshah88]

Homework Statement

Let c be the path c(t)=(2t,t^2,logt), defined for t>0. Find the arc length of c between the points (2,1,0) and (4,4,log2)

I just have a problem with the limits for the integral...what limits so I set for it after finding the derivative and using Pythagorean theorem...thanks.

 

[micromass]

Let's start with the beginning, what's the formula for calculating the arc length??

 

[HallsofIvy]

If your only problem is limits of integration, you want (2t, t^2,ln(t))= (2, 1, 0) for the lower limit, (2t, t^2, ln(t))= (4, 4, ln(2)). Can you solve 2t= 2 and 2t= 4? (Because those points on the curve, those values of t must satisfy t^2= 1, ln(t)= 0 and t^2= 4, ln(t)= 1, respectively.