General question on arc length of a plane curve (the book isn't very clear). I have two functions, g(t) and f(t) in the form x= and y=, respectively on an interval a

Question

General question on arc length of a plane curve (the book isn't very clear). I have two functions, g(t) and f(t) in the form x= and y=, respectively on an interval a < t < b. Given the integral from a to b of f(t) dt, what is f(t)?

anonymous · Answer

Here's the integral:
$$\int\limits_{a}^{b} f(t) \space dt$$

ganeshie8 · Answer

you're looking for arc length of a curve in parametric form ?

anonymous · Answer

Yes. I was trying not to be too specific, because I want to work through the problem on my own.

anonymous · Answer

Basically, it's saying "you have the arc length of the plane curve, x=something, y=something where a<=t<b<=t

anonymous · Answer

it is the norm of the derivative of the vector funtion

ganeshie8 · Answer

The arc length of curve $x = f(t), y = g(t)$  between $a\le t\le b$ is :


$\large    \mathbb \int_a^b \sqrt{\left(\frac{dx}{dt}\right)^2 +
\left(\frac{dy}{dt}\right)^2 }~dt$

anonymous · Answer

^^this is what I was trying to say, idk how to write equations :D

anonymous · Answer

Ah, now that makes sense! Between the labored 30 minute explanation on video from class, WeBWorK and an awful text, I thought I'd never figure it out. THANK YOU! I think I'd better hang out more here, I waste to much time torturing myself to no answer. :)

anonymous · Answer

also be careful with you f(t) and parameterizations because you need to use unique variables :P

anonymous · Answer

Correction "too much time". :) Thanks again.

ganeshie8 · Answer

yeah... @sylbot :) use latex for equations : http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)

ganeshie8 · Answer

good to hear :) u wlc !!