find the length of the curve

I would begin with the formula:

\(\displaystyle \displaystyle s=\int_a^b\sqrt{\left(x'(t) \right)^2+\left(y'(t) \right)^2+\left(z'(t) \right)^2}\,dt\)
 
blazekid43 said:
I'm completely lost in this question, how do I find the length of the curve?

View attachment 3104

thanks
Click to expand...
All three of these problems involve parametric curves in three dimensions. You can imagine yourself moving along with position at time t given by the vector r(t). Let ds be the distance you move in a time increment dt.

\(\displaystyle \displaystyle ds = \left[\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2 + \left(\frac{dz}{dt}\right)^2 \right]^{1/2}\ dt \)

The total distance is the integral of \(\displaystyle ds\) over the stated interval of \(\displaystyle t\).

Show us your work so we can see where you are getting stuck!
 
following the formula you provided me,

I ended up with the equation:

<a href="http://www.codecogs.com/eqnedit.php?latex=\dpi{150}&space;s&space;=\begin{bmatrix}\sqrt{{\frac{16}{7t}t^3}&plus;e^2^t-e^-^2^t}&space;\,&space;\,&space;\,&space;\end{bmatrix}^3_0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\dpi{150}&space;s&space;=\begin{bmatrix}\sqrt{{\frac{16}{7t}t^3}&plus;e^2^t-e^-^2^t}&space;\,&space;\,&space;\,&space;\end{bmatrix}^3_0" title="s =\begin{bmatrix}\sqrt{{\frac{16}{7t}t^3}+e^2^t-e^-^2^t} \, \, \, \end{bmatrix}^3_0" /></a>

It takes so long to create these equations on the online generator things...
 
blazekid43 said:
following the formula you provided me,

I ended up with the equation:

<a href="http://www.codecogs.com/eqnedit.php?latex=\dpi{150}&space;s&space;=\begin{bmatrix}\sqrt{{\frac{16}{7t}t^3}&plus;e^2^t-e^-^2^t}&space;\,&space;\,&space;\,&space;\end{bmatrix}^3_0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\dpi{150}&space;s&space;=\begin{bmatrix}\sqrt{{\frac{16}{7t}t^3}&plus;e^2^t-e^-^2^t}&space;\,&space;\,&space;\,&space;\end{bmatrix}^3_0" title="s =\begin{bmatrix}\sqrt{{\frac{16}{7t}t^3}+e^2^t-e^-^2^t} \, \, \, \end{bmatrix}^3_0" /></a>

It takes so long to create these equations on the online generator things...
Click to expand...

Write it by hand - scan it - add the image using editing-tools provided in the "reply to thread" box.
 
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