An engineering student watches an ant walk continuously along a wire for 1 minute. The shape of the wire can be given by the function f(t)=2t^2. Find the length (in meters) that the ant walked along the wire.

Question

anonymous · Answer

Are we assuming t is in seconds and not minutes?

anonymous · Answer

The first thing you gotta do is to to find a function that describas de lenght of the curve you can do that either by a line integral or a  find the legth path by some integration formual

anonymous · Answer

Using
$$L=\int\limits_{a}^{b}\sqrt{1+[f \prime(x)]^2}dx$$
I get to $$L=\int\limits_{0}^{60}\sqrt{1+6t^2}dt$$
And get stuck because I can't think of any trig substitution to complete the integral. So unfortunately I don't know...

anonymous · Answer

6 is supposed to be 16 fyi

anonymous · Answer

the integral cant be solve using a trig substitution which becomes $$\int\limits_{}^{}\sec ^{3}xdx$$ then by  integration by parts you can solve it

$$\int\limits_{}^{}secx*\sec ^{2}dx$$
     U             dv

anonymous · Answer

thats the way to solve it

anonymous · Answer

althoug I will recommend to solve this integral with the reduction formula Here is a great tool to solve any type of integral http://www.wolframalpha.com/input/?i=integrate+&a=*C.integrate-_*Calculator.dflt-&f2=sqrt%281%2B4t^2%29&x=9&y=3&f=Integral.integrand_sqrt%281%2B6t^2%29&a=*FVarOpt.1-_**-.***Integral.rangestart-.*Integral.rangeend--.**Integral.variable---.*--

anonymous · Answer

from what I see you are just telling us the time and the "shape"  of the path taken , but we might need some information regarding the position (s(t))or velocity(v(t))